C₇×#23794 #13201010

order	1792
nilpotency class	3
isoclinism	isoclinic class of #2010
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₇×#23794

Subgroups

	subgroup	G/H
center	C₇×C₈	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂×C₇	#2397
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₇×C₈ ◁ C₂²×C₇×C₈ ◁ G

930 conjugacy classes of subgroups; only the 250 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 250 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)(8,9,12,16,13,17,25,31)(10,18,20,26,21,30,24,14)(11,15,22,28,23,29,36,39)(19,32,33,37,34,38,35,27);(8,10)(9,14)(11,19)(12,24)(13,21)(15,27)(16,30)(17,26)(18,31)(20,25)(22,35)(23,34)(28,38)(29,37)(32,39)(33,36);(14,26)(18,30)(27,37)(32,38);(8,11,12,22,13,23,25,36)(9,15,16,28,17,29,31,39)(10,19,24,35,21,34,20,33)(14,27,30,38,26,37,18,32)

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 16782);