C₂×C₇×D₁₀₈₃ #44476479

order	30324
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₇×D₁₀₈₃
unambiguous semidirect product	(C₂×C₃)⋊(C₇×D₃₆₁)
unambiguous semidirect product	(C₂×C₃₆₁)⋊(D₃×C₇)

Splittings

Fitting	C₂×C₃×C₇×C₃₆₁ ⋊ C₂
derived, Hall	C₃×C₃₆₁ ⋊ C₂²×C₇
Hall	C₃×C₇×C₃₆₁ ⋊ C₂²
Hall	C₇×C₃₆₁ ⋊ C₂×D₃
Sylow	C₃₆₁ ⋊ C₂×D₃×C₇
Hall	C₃×C₇ ⋊ C₂×D₃₆₁
Sylow	C₃ ⋊ C₂×C₇×D₃₆₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₇	D₁₀₈₃
commutator, cosocle, hypocenter	C₃×C₃₆₁	C₂²×C₇
Frattini	C₁₉	C₂×C₇×D₅₇
Fitting	C₂×C₃×C₇×C₃₆₁	C₂
socle	C₂×C₃×C₇×C₁₉	D₁₉
LCS	G ▷ C₃×C₃₆₁
UCS	C₁ ◁ C₂×C₇

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 373
transitive degree	μ_t(G) = 15162

A minimal faithful permutation representation — 2 generators on 373 points:

(4,5)(6,7,8,9,10,11,12)(14,16)(15,19)(17,22)(18,25)(20,28)(21,27)(23,32)(24,35)(26,37)(29,41)(30,40)(31,39)(33,46)(34,49)(36,51)(38,53)(42,58)(43,57)(44,56)(45,55)(47,64)(48,67)(50,69)(52,71)(54,73)(59,79)(60,78)(61,77)(62,76)(63,75)(65,86)(66,89)(68,91)(70,93)(72,95)(74,97)(80,104)(81,103)(82,102)(83,101)(84,100)(85,99)(87,112)(88,115)(90,117)(92,119)(94,121)(96,123)(98,125)(105,133)(106,132)(107,131)(108,130)(109,129)(110,128)(111,127)(113,142)(114,145)(116,147)(118,149)(120,151)(122,153)(124,155)(126,157)(134,166)(135,165)(136,164)(137,163)(138,162)(139,161)(140,160)(141,159)(143,176)(144,179)(146,181)(148,183)(150,185)(152,187)(154,189)(156,191)(158,193)(167,203)(168,202)(169,201)(170,200)(171,199)(172,198)(173,197)(174,196)(175,195)(177,178)(180,214)(182,216)(184,218)(186,220)(188,222)(190,224)(192,226)(194,228)(204,229)(205,237)(206,236)(207,235)(208,234)(209,233)(210,232)(211,231)(212,230)(213,246)(215,248)(217,250)(219,252)(221,254)(223,256)(225,258)(227,260)(238,261)(239,268)(240,267)(241,266)(242,265)(243,264)(244,263)(245,262)(247,276)(249,278)(251,280)(253,282)(255,284)(257,286)(259,288)(269,289)(270,295)(271,294)(272,293)(273,292)(274,291)(275,290)(277,302)(279,304)(281,306)(283,308)(285,310)(287,312)(296,313)(297,318)(298,317)(299,316)(300,315)(301,314)(303,324)(305,326)(307,328)(309,330)(311,332)(319,333)(320,337)(321,336)(322,335)(323,334)(325,342)(327,344)(329,346)(331,348)(338,349)(339,352)(340,351)(341,350)(343,356)(345,358)(347,360)(353,361)(354,363)(355,362)(357,366)(359,368)(364,369)(365,370)(367,372)(371,373);(1,2)(3,4,5)(13,57,164,289,223,150,88,196,315,370,355,274,141,147,220,286,239,107,30,19,78,201,259,188,118,65,232,335,373,341,244,112,183,254,312,206,82,21,28,103,237,225,152,90,127,264,351,367,323,211,145,218,284,296,170,61,16,41,132,261,190,120,66,160,292,363,357,301,175,181,252,310,270,137,44,25,58,165,227,154,92,47,197,316,369,343,275,142,216,282,332,240,108,31,37,79,202,192,122,68,99,233,336,359,325,245,179,250,308,319,207,83,22,53,104,229,156,94,48,128,265,352,345,303,212,214,280,330,297,171,62,35,73,133,194,124,70,33,161,293,361,327,277,176,248,306,348,271,138,45,51,97,166,158,96,50,75,198,317,347,305,247,177,278,328,338,241,109,32,71,125,203,126,72,34,100,234,337,329,279,213,246,304,346,320,208,84,49,95,157,167,98,52,23,129,266,349,307,249,178,276,326,360,298,172,63,69,123,193,134,74,36,55,162,294,331,281,215,143,302,344,353,272,139,46,93,155,228,105,54,24,76,199,318,309,251,180,230,324,358,339,242,110,67,121,191,204,80,38,17,101,235,333,283,217,144,262,342,368,321,209,85,91,153,226,168,59,26,39,130,267,311,253,182,113,290,356,364,299,173,64,119,189,260,135,42,18,56,163,295,285,219,146,195,314,366,354,273,140,89,151,224,238,106,29,14,77,200,313,255,184,114,231,334,372,340,243,111,117,187,258,205,81,20,27,102,236,287,221,148,87,263,350,371,322,210,86,149,222,288,169,60,15,40,131,268,257,186,116,159,291,362,365,300,174,115,185,256,269,136,43)

Conjugacy classes & character table

7602 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30324, 62);

C2×C7×D1083 #44476479