D₄₇×#2913 #27079946

order	12032
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

D₄₇×#2913

Splittings

Fitting	C₄₇×#2913 ⋊ C₂
Sylow	C₄₇ ⋊ C₂×#2913

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#2913	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂×#41×D₄₇	C₂²
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2913	D₄₇
hypocenter	C₄₇	C₂×#2913
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×#41 ◁ #2913

2766 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 67
transitive degree	μ_t(G) = 3008

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

(7,14)(12,19)(15,18)(16,20)(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);(5,7)(6,12)(8,15)(9,14)(10,16)(11,18)(13,19)(17,20);(5,6,11,17,9,13,8,10)(7,12,18,20,14,19,15,16);(1,2,3,4)(6,10)(8,11)(12,16)(13,17)(15,18)(19,20);(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

1100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1033236);

D47×#2913 #27079946