D₄₇×#3267 #27091267

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

Aliases

direct product

D₄₇×#3267

Splittings

Fitting	C₄₇×#3267 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#3267

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3267	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3267	D₄₇
hypocenter	C₄₇	C₂×#3267
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #3267

2914 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 1504

A minimal faithful permutation representation — 5 generators on 67 points:

(6,12)(8,16)(10,13)(11,18)(14,20)(17,19)(21,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23);(2,4)(5,7,9,15)(6,11,13,19)(8,14,16,20)(10,17,12,18);(5,6)(7,11)(8,12)(9,13)(10,16)(14,18)(15,19)(17,20);(1,2)(3,4)(6,10)(8,16)(11,17)(12,13)(14,20)(18,19);(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)(64,65)(66,67)

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, 1044557);

D47×#3267 #27091267