C₁₃×#17307 #15703646

order	3328
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#17307

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

1014 conjugacy classes of subgroups; only the 318 normal subgroups are shown.

normal subgroups only

This group has 1014 conjugacy classes of subgroups — too many to draw. Only its 318 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) = 3328

A minimal faithful permutation representation — 4 generators on 45 points:

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

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 10295);