C₃²×#1791 #11768840

order	1152
nilpotency class	3
isoclinism	isoclinic class of B(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₄ · Schur multiplier (H₂) = C₂⁵×C₃

Aliases

direct product

C₃²×#1791

Subgroups

	subgroup	G/H
center	C₃²×C₄	#120
commutator	C₂³	C₂²×C₃²×C₄
Frattini, cosocle	C₂²×C₄	C₂³×C₃²
socle	C₂×C₃²	#379
prime radical	C₃²×#585	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃²×C₄ ◁ C₂²×C₃²×C₄ ◁ G

1644 conjugacy classes of subgroups; only the 396 normal subgroups are shown.

normal subgroups only

This group has 1644 conjugacy classes of subgroups — too many to draw. Only its 396 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)(7,8,11,16,12,15,24,29)(9,17,20,30,19,13,23,26)(10,14,22,27,21,28,34,38)(18,25,33,36,32,31,35,37);(4,5,6)(7,9)(8,13)(10,18)(11,23)(12,19)(14,25)(15,17)(16,30)(20,24)(21,32)(22,35)(26,29)(27,37)(28,31)(33,34)(36,38);(7,10)(8,14)(9,18)(11,22)(12,21)(13,25)(15,28)(16,27)(17,31)(19,32)(20,33)(23,35)(24,34)(26,36)(29,38)(30,37)

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, 2851);