C₉×#3028 #11767749

order	1152
nilpotency class	3
isoclinism	isoclinic class of #3026
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₉×#3028

Subgroups

	subgroup	G/H
center	C₂×C₉	C₂×#120
commutator	C₂³	C₂⁴×C₉
Frattini, cosocle	C₂³×C₃	C₂⁴×C₃
socle	C₂×C₃	C₂×C₃×#120
prime radical	C₃×#585	C₂×C₃
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₉ ◁ C₂²×C₄×C₉ ◁ G

1074 conjugacy classes of subgroups; only the 318 normal subgroups are shown.

normal subgroups only

This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 318 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 — 4 generators on 41 points:

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

Conjugacy classes & character table

261 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 1760);