D₄₇×#3292 #27092499

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

D₄₇×#3292

Splittings

Fitting	C₄₇×#3292 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3292

Subgroups

	subgroup	G/H
center	C₂	D₄²×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3292	C₂
socle	C₂×C₄₇	C₂×D₄²
hypercenter	#3292	D₄₇
hypocenter	C₄₇	C₂×#3292
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #3292

2766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 752

A minimal faithful permutation representation — 5 generators on 63 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1045789);

D47×#3292 #27092499