C₂×#108×C₄₇ #15688684

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

Aliases

direct product

C₂×#108×C₄₇

Subgroups

	subgroup	G/H
center	C₂×C₄×C₄₇	D₄
commutator	C₄	C₂²×C₄×C₄₇
Frattini, cosocle	C₂×C₄	C₂³×C₄₇
socle	C₂²×C₄₇	C₄⋊C₄
prime radical	C₂³×C₄₇	Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ C₂²×C₄×C₄₇ ◁ G

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 1504

A minimal faithful permutation representation — 3 generators on 65 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65);(3,4,7,10,8,11,6,16)(5,12,14,17,15,18,13,9);(3,5,6,13,8,15,7,14)(4,9,10,12,11,17,16,18)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₇×#1381, C₄₇×#1382, C₄₇×#1383, …
maximal normal subgroup of	C₄₇×#1381, C₄₇×#1382, C₄₇×#1383, …
maximal quotient of	C₂×C₄₇×#334, C₂×C₄₇×#335, C₄₇×#1564, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 110);

C2×#108×C47 #15688684