C₇×#9333 #13186549

order	1792
nilpotency class	3
isoclinism	isoclinic class of #9331
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇×#9333

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇	#386
commutator	C₂²×C₄	C₂²×C₄×C₇
Frattini, cosocle	C₂×C₄²	C₂³×C₇
prime radical	C₇×#3213	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄²×C₇ ◁ G

438 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 448

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

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

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, 2321);