C₃²×#2103 #11769152

order	1152
nilpotency class	3
isoclinism	isoclinic class of #2031
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product

C₃²×#2103

Subgroups

	subgroup	G/H
center	C₃²×C₄	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃²
socle	C₂×C₃²	#400
prime radical	C₂³×C₃²	C₂×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃²×C₄ ◁ C₂²×C₃²×C₄ ◁ G

444 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 38
transitive degree	μ_t(G) = 288

A minimal faithful permutation representation — 3 generators on 38 points:

(1,2,3)(7,8,11,16,12,17,13,28)(9,18,20,30,22,33,21,14)(10,23,25,37,26,15,27,32)(19,31,34,38,35,36,24,29);(4,5,6)(7,9,13,20,12,22,11,21)(8,14,28,18,17,30,16,33)(10,24,27,19,26,34,25,35)(15,31,37,38,23,36,32,29);(7,10,11,25,12,26,13,27)(8,15,16,32,17,23,28,37)(9,19,20,34,22,35,21,24)(14,29,18,31,30,38,33,36)

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, 3163);