C₇×#13350 #13190566

order	1792
nilpotency class	4
isoclinism	isoclinic class of #13350
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₇×#13350

Subgroups

	subgroup	G/H
center, socle	C₂×C₇	#2021
commutator, Frattini, cosocle	C₂×#41	C₂³×C₇
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇ ◁ C₂×C₄×C₇ ◁ C₂×C₇×#41 ◁ G

738 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 94 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 — 3 generators on 39 points:

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

Conjugacy classes & character table

196 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 6338);