C₄₇×#431 #15688686

order	3008
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₄₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₄₇×#431

Subgroups

	subgroup	G/H
center	C₄²×C₄₇	C₂²
commutator	C₂	C₂²×C₈×C₄₇
Frattini, cosocle	C₂×C₄	C₂³×C₄₇
socle	C₂²×C₄₇	C₂²×C₄
prime radical	C₂³×C₄₇	C₂×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₄₇ ◁ G

118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 63
transitive degree	μ_t(G) = 1504

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)(50,53)(51,52)(54,55)(56,57,58,60,59,61,62,63);(49,52)(53,55);(48,50,51,54)(49,53,52,55)

Conjugacy classes & character table

1880 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄₇×#1274, C₄₇×#1275, C₄₇×#1276, …
maximal normal subgroup of	C₄₇×#1274, C₄₇×#1275, C₄₇×#1276, …
maximal quotient of	C₄₇×#1744, C₄×C₂²⋊C₈×C₄₇, C₄×C₄⋊C₈×C₄₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 112);

C47×#431 #15688686