C₂×C₅×D₁₇₉₃ #49089599

order	35860
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×D₁₇₉₃
unambiguous semidirect product	(C₂×C₁₆₃)⋊(C₅×D₁₁)

Splittings

Fitting, socle	C₂×C₅×C₁₁×C₁₆₃ ⋊ C₂
derived, Hall	C₁₁×C₁₆₃ ⋊ C₂²×C₅
Hall	C₅×C₁₁×C₁₆₃ ⋊ C₂²
Hall	C₅×C₁₆₃ ⋊ C₂×D₁₁
Sylow	C₁₆₃ ⋊ C₂×C₅×D₁₁
Hall	C₅×C₁₁ ⋊ C₂×D₁₆₃
Sylow	C₁₁ ⋊ C₂×C₅×D₁₆₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₇₉₃
commutator, cosocle, hypocenter	C₁₁×C₁₆₃	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₁×C₁₆₃	C₂
LCS	G ▷ C₁₁×C₁₆₃
UCS	C₁ ◁ C₂×C₅

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 181
transitive degree	μ_t(G) = 17930

A minimal faithful permutation representation — 2 generators on 181 points:

(3,4,5,6,7)(9,10)(11,12)(13,14)(15,16)(17,18)(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);(1,2)(8,9,11,13,15,17,18,16,14,12,10)(19,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108,110,112,114,116,118,120,122,124,126,128,130,132,134,136,138,140,142,144,146,148,150,152,154,156,158,160,162,164,166,168,170,172,174,176,178,180,181,179,177,175,173,171,169,167,165,163,161,159,157,155,153,151,149,147,145,143,141,139,137,135,133,131,129,127,125,123,121,119,117,115,113,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21)

Conjugacy classes & character table

8980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35860, 32);

C2×C5×D1793 #49089599