C₇×#8753 #13185969

order	1792
nilpotency class	3
isoclinism	isoclinic class of #8746
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇×#8753

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇	#381
commutator	C₂⁴	C₂²×C₄×C₇
Frattini, cosocle	C₂³×C₄	C₂³×C₇
prime radical	C₂⁴×C₇	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂³×C₄×C₇ ◁ G

566 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 448

A minimal faithful permutation representation — 3 generators on 47 points:

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

Conjugacy classes & character table

238 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1741);