C₉×#1293 #11766014

order	1152
nilpotency class	3
isoclinism	isoclinic class of #1284
automorphism	?
homology	Abelianization (H₁) = C₄²×C₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₉×#1293

Subgroups

	subgroup	G/H
center	C₂²×C₉	#95
commutator	C₂×C₄	C₄²×C₉
Frattini, cosocle	C₂³×C₃×C₄	C₂²×C₃
socle	C₂²×C₃	C₃×#95
prime radical	C₂⁴×C₃	C₃×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₂³×C₄×C₉ ◁ G

276 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 288

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

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

Conjugacy classes & character table

288 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 25);