C₉×#2201 #11766922

order	1152
nilpotency class	4
isoclinism	isoclinic class of #2199
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₉×#2201

Subgroups

	subgroup	G/H
center	C₂×C₉	B(4,𝔽₂)
commutator	C₂×D₄	C₂³×C₉
Frattini, cosocle	C₂×C₃×D₄	C₂³×C₃
socle	C₂×C₃	C₃×B(4,𝔽₂)
prime radical	C₃×H(5,𝔽₂)	C₂²×C₃
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₉ ◁ C₂²×C₉ ◁ C₂×D₄×C₉ ◁ G

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

normal subgroups only

This group has 339 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)(12,20)(13,17)(14,18)(15,19)(16,22)(21,37)(23,36)(24,35)(25,31)(26,32)(27,34)(28,38)(29,39)(30,40)(33,41);(10,12,15,23)(11,16,19,29)(13,24,26,21)(14,22,27,39)(17,30,32,28)(18,20,34,36)(25,40,41,38)(31,35,33,37);(10,13,15,26)(11,17,19,32)(12,21,23,24)(14,25,27,41)(16,28,29,30)(18,33,34,31)(20,35,36,37)(22,38,39,40)

Conjugacy classes & character table

153 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 933);