C₇×#23928 #13201144

order	1792
nilpotency class	3
isoclinism	isoclinic class of #23924
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₇×#23928

Subgroups

	subgroup	G/H
center, socle	C₂³×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂²×C₇×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂²×C₇×#41 ◁ G

1696 conjugacy classes of subgroups; only the 302 normal subgroups are shown.

normal subgroups only

This group has 1696 conjugacy classes of subgroups — too many to draw. Only its 302 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) = 47
transitive degree	μ_t(G) = 896

A minimal faithful permutation representation — 4 generators on 47 points:

(1,2,3,4,5,6,7)(8,9)(10,11)(16,17,21,25)(18,22,27,36)(19,29,31,39)(20,32,34,24)(23,33,38,30)(26,40,41,47)(28,44,43,37)(35,45,46,42);(9,11)(12,13)(14,15)(16,18,21,27)(17,22,25,36)(19,26,31,41)(20,28,34,43)(23,35,38,46)(24,37,32,44)(29,40,39,47)(30,42,33,45);(13,15)(16,19,21,31)(17,23,25,38)(18,26,27,41)(20,33,34,30)(22,35,36,46)(24,39,32,29)(28,45,43,42)(37,47,44,40);(9,11)(18,27)(22,36)(26,41)(28,43)(35,46)(37,44)(40,47)(42,45)

Conjugacy classes & character table

322 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 16916);