C₉×#1307 #11766028

order	1152
nilpotency class	3
isoclinism	isoclinic class of #1304
automorphism	?
homology	Abelianization (H₁) = C₄²×C₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₉×#1307

Subgroups

	subgroup	G/H
center	C₂²×C₉	#95
commutator	C₂³	C₄²×C₉
Frattini, cosocle	C₂×C₃×C₄²	C₂²×C₃
socle	C₂²×C₃	C₃×#95
prime radical	C₂³×C₃	C₃×C₄²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄²×C₉ ◁ G

195 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 195 conjugacy classes of subgroups — too many to draw. Only its 96 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) = 576

A minimal faithful permutation representation — 2 generators on 33 points:

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

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, 39);