D₄₇×#3214 #27087557

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

direct product

D₄₇×#3214

Splittings

Fitting	C₄₇×#3214 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3214

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3214	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3214	D₄₇
hypocenter	C₄₇	C₂×#3214
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3214

2446 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 3008

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

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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1040847);

D47×#3214 #27087557