C₄×#131×D₄₇ #27079678

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

direct product

C₄×#131×D₄₇

Splittings

Fitting	C₄×#131×C₄₇ ⋊ C₂
Sylow	C₄₇ ⋊ C₂×C₄×#131

Subgroups

	subgroup	G/H
center	C₄×C₈	C₂²×D₄₇
commutator	C₂×C₄₇	C₂³×C₄²
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄×#131×C₄₇	C₂
socle	C₂²×C₄₇	C₂⁴×C₄
prime radical	C₂×#41×D₄₇	C₂²
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₄×#131	D₄₇
hypocenter	C₄₇	C₂×C₄×#131
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄×C₈ ◁ C₄×#131

3366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 3008

A minimal faithful permutation representation — 5 generators on 67 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);(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)(54,60)(57,63)(61,66)(64,67);(52,54)(53,57)(55,61)(56,60)(58,64)(59,63)(62,66)(65,67);(52,53,55,58,56,59,62,65)(54,57,61,64,60,63,66,67);(48,49,50,51)

Conjugacy classes & character table

2000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1032968);

C4×#131×D47 #27079678