C₉×#2212 #11766933

order	1152
nilpotency class	4
isoclinism	isoclinic class of #2212
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₉×#2212

Subgroups

	subgroup	G/H
center	C₂×C₉	#459
commutator	C₂×C₈	C₂³×C₉
Frattini, cosocle	C₂×C₃×C₈	C₂³×C₃
socle	C₂×C₃	C₃×#459
prime radical	C₃×#509	C₂×C₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₉ ◁ C₂×C₄×C₉ ◁ C₄×C₈×C₉ ◁ G

231 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 231 conjugacy classes of subgroups — too many to draw. Only its 90 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)(12,20)(13,25)(14,29)(15,31)(16,21)(17,23)(18,22)(19,30)(24,38)(26,37)(27,41)(28,33)(32,34)(35,39)(36,40);(10,12,14,23,16,24,30,15)(11,17,19,20,21,31,29,38)(13,22,26,39,28,40,27,32)(18,33,34,37,36,25,35,41);(10,13)(11,18)(12,22)(14,26)(15,32)(16,28)(17,33)(19,34)(20,37)(21,36)(23,39)(24,40)(25,31)(27,30)(29,35)(38,41)

Conjugacy classes & character table

207 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 944);