C₉×#1674 #11766395

order	1152
nilpotency class	3
isoclinism	isoclinic class of #1665
automorphism	?
homology	Abelianization (H₁) = C₂³×C₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₉×#1674

Subgroups

	subgroup	G/H
center	C₂²×C₉	#121
commutator	C₄²	C₂³×C₉
Frattini, cosocle	C₃×C₄²	C₂³×C₃
socle, prime radical	C₂²×C₃	C₃×#121
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₄²×C₉ ◁ G

234 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 108 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) = 33
transitive degree	μ_t(G) = 1152

A minimal faithful permutation representation — 3 generators on 33 points:

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

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, 406);