C₃²×#1718 #11768767

order	1152
nilpotency class	3
isoclinism	isoclinic class of #1714
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₃×C₄

Aliases

direct product

C₃²×#1718

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₃²	#127
commutator, Frattini, cosocle	C₄²	C₂³×C₃²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄² ◁ G

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

normal subgroups only

This group has 492 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) = 1152

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

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

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, 2778);