C₁₃×#17308 #15703647

order	3328
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂³×C₄²

Aliases

direct product

C₁₃×#17308

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

1034 conjugacy classes of subgroups; only the 302 normal subgroups are shown.

normal subgroups only

This group has 1034 conjugacy classes of subgroups — too many to draw. Only its 302 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)(15,18)(16,20)(22,23,25,27)(24,28,29,26)(30,31,34,35)(32,36,37,33)(40,44)(42,45);(15,18)(16,20)(24,29)(26,28)(31,35)(33,36)(38,39,41,43)(40,45,44,42);(14,15,17,18)(16,19,20,21)(22,23)(24,26)(25,27)(28,29)(30,32)(31,36)(33,35)(34,37)(38,40,41,44)(39,42,43,45);(14,16)(15,19)(17,20)(18,21)(22,24,25,29)(23,26,27,28)(30,33,34,36)(31,37,35,32)(38,39)(40,42)(41,43)(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, 10296);