C₉×#2070 #11766791

order	1152
nilpotency class	3
isoclinism	isoclinic class of #2069
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₉×#2070

Subgroups

	subgroup	G/H
center	C₂×C₉	#396
commutator	C₂²×C₄	C₂³×C₉
Frattini, cosocle	C₂²×C₃×C₄	C₂³×C₃
socle	C₂×C₃	C₃×#396
prime radical	C₂³×C₃	C₂×C₃×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₉ ◁ C₂²×C₄×C₉ ◁ G

294 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 120 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)(10,11,14,28,15,19,30,18)(12,20,22,16,23,36,40,32)(13,24,26,33,27,17,29,34)(21,37,38,31,25,35,39,41);(10,12,14,22,15,23,30,40)(11,16,18,20,19,32,28,36)(13,25,26,39,27,21,29,38)(17,31,33,37,24,41,34,35);(10,13,15,27)(11,17,19,24)(12,21,23,25)(14,29,30,26)(16,31,32,41)(18,34,28,33)(20,35,36,37)(22,39,40,38)

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, 802);