D₄₇×#2988 #27081320

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

D₄₇×#2988

Splittings

Fitting	C₄₇×#2988 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#2988

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator	C₂×C₄₇	C₂⁴×C₈
Fitting	C₄₇×#2988	C₂
socle	C₂²×C₄₇	C₂⁴×C₄
prime radical	C₂×#41×D₄₇	C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2988	D₄₇
hypocenter	C₄₇	C₂×#2988
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2988

2434 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:

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

1700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1034610);

D47×#2988 #27081320