C₄₇×#464 #15688719

order	3008
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₄₇×#464

Subgroups

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₄₇
prime radical	C₂×D₄×C₄₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₄²×C₄₇ ◁ G

112 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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)(49,51)(52,53)(54,60)(55,57)(56,64)(58,62)(59,63)(61,67)(65,66);(48,49,50,51)(53,57)(58,66)(59,64)(60,67);(52,54,55,61)(53,58,57,66)(56,65,63,62)(59,67,64,60)

Conjugacy classes & character table

893 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₄₇×#464, C₄₇×#3035, C₄₇×#3037, …
maximal normal subgroup of	C₂×C₄₇×#464, C₄₇×#3035, C₄₇×#3037, …
maximal quotient of	C₄₇×#1678, C₄₇×#1680, C₄₇×#1682, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 145);