C₄₇×#427 #15688682

order	3008
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₄₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₄₇×#427

Subgroups

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

114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 67 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)(48,49,50,51)(52,53)(54,61)(55,59)(56,65)(57,60)(58,63)(62,66)(64,67);(52,54,56,63,57,64,55,62)(53,58,59,61,60,66,65,67);(52,55,57,56)(53,59,60,65)(54,62,64,63)(58,61,66,67)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₇×#1382, C₄₇×#1384, C₄₇×#1386, …
maximal normal subgroup of	C₄₇×#1382, C₄₇×#1384, C₄₇×#1386, …
maximal quotient of	C₄₇×#1564, C₄₇×#1568, C₄₇×#1572, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 108);

C47×#427 #15688682