C₁₃×#11917 #15698256

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11915
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#11917

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1533
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	#97	C₂³×C₁₃
prime radical	C₁₃×#532	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×M₁₆ ◁ G

280 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 90 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)(14,15,18,22,17,23,30,41,19,24,34,42,31,21,33,39)(16,25,27,43,28,20,35,37,29,36,44,40,26,38,32,45);(14,16)(15,20)(17,26)(18,32)(19,29)(21,36)(22,40)(23,25)(24,38)(27,33)(28,31)(30,44)(34,35)(37,41)(39,45)(42,43);(14,17,19,31)(15,21,24,23)(16,26,29,28)(18,33,34,30)(20,36,38,25)(22,41,42,39)(27,35,44,32)(37,43,45,40)

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 4905);