C₉×#2017 #11766738

order	1152
nilpotency class	3
isoclinism	isoclinic class of #2010
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₉×#2017

Subgroups

	subgroup	G/H
center	C₄×C₉	#127
commutator	C₂²×C₄	C₂³×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂×C₃	C₃×#392
prime radical	C₃×#2017	C₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₉ ◁ C₂²×C₄×C₉ ◁ G

525 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 525 conjugacy classes of subgroups — too many to draw. Only its 132 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)(12,21)(13,26)(14,31)(15,19)(16,20)(17,23)(18,29)(22,39)(24,34)(25,33)(27,38)(28,37)(30,36)(32,40)(35,41);(10,12)(11,17)(13,27)(14,24)(15,23)(16,25)(18,35)(19,33)(20,34)(21,31)(22,28)(26,32)(29,40)(30,41)(36,39)(37,38);(10,13)(11,18)(12,22)(14,28)(15,29)(16,30)(17,32)(19,36)(20,37)(21,38)(23,27)(24,41)(25,40)(26,31)(33,35)(34,39)

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 749);