C₃²×#2242 #11769291

order	1152
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃² · Schur multiplier (H₂) = C₃×C₄

Aliases

direct product

C₃²×#2242

Subgroups

	subgroup	G/H
center, socle	C₂²×C₃²	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃²
prime radical	C₂×C₃²×D₈	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄² ◁ C₃²×C₄×C₈ ◁ G

414 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 192 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) = 46
transitive degree	μ_t(G) = 576

A minimal faithful permutation representation — 3 generators on 46 points:

(1,2,3)(7,8)(9,12)(10,11)(13,14)(15,16)(17,29)(18,23)(19,37)(20,40)(21,41)(22,28)(24,33)(25,30)(26,39)(27,38)(31,43)(32,42)(34,46)(35,45)(36,44);(4,5,6)(8,11)(12,14)(15,17,30,35,21,32,39,36,22,33,20,31,38,34,19,18)(16,23,37,46,27,43,40,24,28,44,26,42,41,45,25,29);(7,9,10,13)(8,12,11,14)(15,18,19,34,38,31,20,33,22,36,39,32,21,35,30,17)(16,24,25,43,41,46,26,23,28,29,40,45,27,42,37,44)

Conjugacy classes & character table

342 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 3302);