C₁₃×#11847 #15698186

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11753
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#11847

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₃
prime radical	C₁₃×#392	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

432 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 45
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 45 points:

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

Conjugacy classes & character table

481 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 4835);