C₉×#2239 #11766960

order	1152
nilpotency class	4
isoclinism	isoclinic class of #2238
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₉×#2239

Subgroups

	subgroup	G/H
center	C₂×C₉	#481
commutator	C₂×C₈	C₂³×C₉
Frattini, cosocle	C₂×C₃×C₈	C₂³×C₃
socle	C₂×C₃	C₃×#481
prime radical	C₂³×C₃	C₃×SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₄×C₉ ◁ C₂×C₉×M₁₆ ◁ G

186 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 84 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) = 41
transitive degree	μ_t(G) = 288

A minimal faithful permutation representation — 3 generators on 41 points:

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 971);