C₄₇×#443 #15688698

order	3008
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₄₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₄₇×#443

Subgroups

	subgroup	G/H
center	C₈×C₄₇	D₄
commutator	C₄	C₂²×C₄×C₄₇
Frattini, cosocle	C₂×C₄	C₂³×C₄₇
socle	C₂×C₄₇	C₄×D₄
prime radical	#135×C₄₇	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₄₇ ◁ C₂×C₈×C₄₇ ◁ G

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 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)(48,49,52,56,53,50,57,55)(51,54,59,62,60,58,63,61);(48,50)(49,53)(51,58)(52,55)(54,60)(56,57)(59,61)(62,63);(48,51,52,59,53,60,57,63)(49,54,56,62,50,58,55,61)

Conjugacy classes & character table

1316 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄₇×#1335, C₄₇×#1336, C₄₇×#2170, …
maximal normal subgroup of	C₄₇×#1335, C₄₇×#1336, C₄₇×#2170, …
maximal quotient of	C₈×D₈×C₄₇, C₈×SD₁₆×C₄₇, C₈×Q₁₆×C₄₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 124);

C47×#443 #15688698