D₄₇×#3105 #27084319

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

Aliases

direct product

D₄₇×#3105

Splittings

Fitting	C₄₇×#3105 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3105

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3105	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#447×D₄₇	C₂
hypercenter	#3105	D₄₇
hypocenter	C₄₇	C₂×#3105
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3105

2602 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 1504

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

(1,3,4,7)(2,6,5,8)(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);(10,14)(12,16)(13,15);(2,5)(6,8)(10,13)(14,15);(1,2)(3,6)(4,5)(7,8)(9,10)(11,13)(12,14)(15,16);(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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1037609);

D47×#3105 #27084319