C₂³×#13093957 #27079922

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰

Aliases

direct product

C₂³×#13093957

Splittings

Sylow

C₄₇ ⋊ C₂³×#107

Subgroups

	subgroup	G/H
center	C₂⁵	C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂³×C₄⋊C₄×C₄₇	C₂
socle, prime radical	C₂⁵×C₄₇	D₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂³×C₄⋊C₄	D₄₇
hypocenter	C₄₇	C₂³×#107
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×C₄ ◁ C₂³×C₄⋊C₄

3614 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 12032

A minimal faithful permutation representation — 5 generators on 65 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)(58,59,63,65,61,64,60,62);(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)(54,55,56,57)(59,62)(60,63)(64,65);(52,53);(50,51);(48,49)

Conjugacy classes & character table

1952 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1033212);

C23×#13093957 #27079922