C₇×#23896 #13201112

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

Aliases

direct product

C₇×#23896

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

1764 conjugacy classes of subgroups; only the 282 normal subgroups are shown.

normal subgroups only

This group has 1764 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)(10,14)(11,15)(12,16)(13,17)(18,24)(19,25)(20,26)(21,34)(22,29)(23,30)(27,32)(28,35)(31,38)(33,37)(36,39);(8,10,13,20)(9,14,17,26)(11,18,22,32)(12,19,23,33)(15,27,29,24)(16,25,30,37)(21,31,35,39)(28,38,34,36);(8,11)(9,15)(10,18)(12,21)(13,22)(14,24)(16,28)(17,29)(19,31)(20,32)(23,35)(25,36)(26,27)(30,34)(33,39)(37,38);(8,12)(9,16)(10,19)(11,21)(13,23)(14,25)(15,28)(17,30)(18,31)(20,33)(22,35)(24,36)(26,37)(27,38)(29,34)(32,39)

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, 16884);