C₇×#10645 #13187861

order	1792
nilpotency class	3
isoclinism	isoclinic class of #10645
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₇×#10645

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇	#397
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₇
prime radical	C₇×#532	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄²×C₇ ◁ G

258 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 896

A minimal faithful permutation representation — 3 generators on 39 points:

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

Conjugacy classes & character table

217 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 3633);