C₂×#20257851 #27123905

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹³

Aliases

direct product

C₂×#20257851

Splittings

Fitting	C₂×C₄₇×#554 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3554

Subgroups

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×#554	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#554	D₄₇
hypocenter	C₄₇	C₂×#3554
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#554

7182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 6 generators on 73 points:

(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)(50,52,53,56)(51,55,54,57);(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)(51,54)(55,57)(59,65)(63,72)(64,68)(71,73);(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)(58,61,62,70)(59,64,65,68)(60,66,67,69)(63,71,72,73);(50,51)(52,55)(53,54)(56,57)(58,60,62,67)(59,63,65,72)(61,69,70,66)(64,73,68,71);(51,54)(52,56)(58,59)(60,63)(61,68)(62,65)(64,70)(66,73)(67,72)(69,71);(48,49)

Conjugacy classes & character table

1226 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1077195);

C2×#20257851 #27123905