C₂×#20255432 #27092877

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂×#20255432

Splittings

Fitting	C₂×C₄₇×#451 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3312

Subgroups

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#451	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×C₂²⋊D₄₇	D₄
hypercenter	C₂×#451	D₄₇
hypocenter	C₄₇	C₂×#3312
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#451

2094 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 6016

A minimal faithful permutation representation — 5 generators on 73 points:

(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)(52,57)(54,56);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(58,61,63,70)(59,65,66,73)(60,67,62,69)(64,72,71,68);(50,52)(51,54)(53,57)(55,56)(58,60,63,62)(59,64,66,71)(61,69,70,67)(65,68,73,72);(50,51,53,55)(52,56,57,54)(58,59)(60,64)(61,68)(62,71)(63,66)(65,67)(69,73)(70,72);(48,49)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1046167);

C2×#20255432 #27092877