C₄₇×#568 #15688823

order	3008
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₄₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₄₇×#568

Subgroups

	subgroup	G/H
center	C₄×C₄₇	C₂⁴
commutator	C₂	C₂³×C₄×C₄₇
Frattini, cosocle	C₄	C₂⁴×C₄₇
socle	C₂×C₄₇	C₂³×C₄
prime radical	C₂×#41×C₄₇	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₄₇ ◁ G

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 752

A minimal faithful permutation representation — 4 generators on 63 points:

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

Conjugacy classes & character table

1598 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄₇×#1858, C₄₇×#1861, C₄₇×#1868, …
maximal normal subgroup of	C₄₇×#1858, C₄₇×#1861, C₄₇×#1868, …
maximal quotient of	C₄₇×#2873, C₄₇×#2875, C₄₇×#2879, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 249);

C47×#568 #15688823