C₇×#23899 #13201115

order	1792
nilpotency class	3
isoclinism	isoclinic class of #23897
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₇×#23899

Subgroups

	subgroup	G/H
center, socle	C₂×C₇	#2403
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇ ◁ C₂²×C₄×C₇ ◁ G

1672 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 1672 conjugacy classes of subgroups — too many to draw. Only its 282 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) = 39
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 4 generators on 39 points:

(1,2,3,4,5,6,7)(8,9)(10,18)(11,15)(12,24)(13,17)(14,21)(16,27)(19,35)(20,32)(22,33)(23,31)(25,28)(26,30)(29,37)(34,36)(38,39);(14,28)(18,32)(29,39)(34,35);(8,10)(9,14)(11,19)(12,25)(13,20)(15,29)(16,32)(17,28)(18,24)(21,27)(22,38)(23,36)(26,37)(30,34)(31,39)(33,35);(8,11,13,23)(9,15,17,31)(10,19,20,36)(12,26,27,22)(14,29,28,39)(16,33,24,30)(18,34,32,35)(21,38,25,37)

Conjugacy classes & character table

280 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 16887);