D₁₅₄₄₇ #44525329

order	30894
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₅₄₄₇
unambiguous semidirect product	C₃⋊D₅₁₄₉
unambiguous semidirect product	C₁₉⋊D₈₁₃
unambiguous semidirect product	C₂₇₁⋊D₅₇

Splittings

Fitting, socle, derived, Hall	C₃×C₁₉×C₂₇₁ ⋊ C₂
Hall	C₁₉×C₂₇₁ ⋊ D₃
Hall	C₃×C₂₇₁ ⋊ D₁₉
Sylow	C₂₇₁ ⋊ D₅₇
Hall	C₃×C₁₉ ⋊ D₂₇₁
Sylow	C₁₉ ⋊ D₈₁₃
Sylow	C₃ ⋊ D₅₁₄₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₉×C₂₇₁	C₂
LCS	G ▷ C₃×C₁₉×C₂₇₁
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 293
transitive degree	μ_t(G) = 15447

A minimal faithful permutation representation — 2 generators on 293 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293);(2,3)(5,22)(6,21)(7,20)(8,19)(9,18)(10,17)(11,16)(12,15)(13,14)(24,293)(25,292)(26,291)(27,290)(28,289)(29,288)(30,287)(31,286)(32,285)(33,284)(34,283)(35,282)(36,281)(37,280)(38,279)(39,278)(40,277)(41,276)(42,275)(43,274)(44,273)(45,272)(46,271)(47,270)(48,269)(49,268)(50,267)(51,266)(52,265)(53,264)(54,263)(55,262)(56,261)(57,260)(58,259)(59,258)(60,257)(61,256)(62,255)(63,254)(64,253)(65,252)(66,251)(67,250)(68,249)(69,248)(70,247)(71,246)(72,245)(73,244)(74,243)(75,242)(76,241)(77,240)(78,239)(79,238)(80,237)(81,236)(82,235)(83,234)(84,233)(85,232)(86,231)(87,230)(88,229)(89,228)(90,227)(91,226)(92,225)(93,224)(94,223)(95,222)(96,221)(97,220)(98,219)(99,218)(100,217)(101,216)(102,215)(103,214)(104,213)(105,212)(106,211)(107,210)(108,209)(109,208)(110,207)(111,206)(112,205)(113,204)(114,203)(115,202)(116,201)(117,200)(118,199)(119,198)(120,197)(121,196)(122,195)(123,194)(124,193)(125,192)(126,191)(127,190)(128,189)(129,188)(130,187)(131,186)(132,185)(133,184)(134,183)(135,182)(136,181)(137,180)(138,179)(139,178)(140,177)(141,176)(142,175)(143,174)(144,173)(145,172)(146,171)(147,170)(148,169)(149,168)(150,167)(151,166)(152,165)(153,164)(154,163)(155,162)(156,161)(157,160)(158,159)

Polycyclic presentation:

2,3,19,271|b^a=b^2,c^a=c^18,d^a=d^270

Conjugacy classes & character table

7725 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₅₄₄₇
maximal normal subgroup of	C₂×D₁₅₄₄₇
maximal quotient of	Dic₁₅₄₄₇, C₂×D₁₅₄₄₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30894, 12);

D15447 #44525329