C₇×#23895 #13201111

order	1792
nilpotency class	3
isoclinism	isoclinic class of #23895
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₇×#23895

Subgroups

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

2002 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 2002 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) = 23
transitive degree	μ_t(G) = 112

A minimal faithful permutation representation — 4 generators on 23 points:

(1,2,3,4,5,6,7)(8,9)(10,13)(11,14)(12,15)(16,22)(17,19)(18,21)(20,23);(13,19)(20,22);(8,10)(9,13)(11,16)(12,17)(14,20)(15,19)(18,23)(21,22);(8,11)(9,14)(10,16)(12,18)(13,20)(15,21)(17,23)(19,22)

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, 16883);