C₁₃×#17301 #15703640

order	3328
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₃×#17301

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

926 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 926 conjugacy classes of subgroups — too many to draw. Only its 286 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)(19,21)(22,23,25,27)(24,26,28,29)(30,31)(32,35)(33,34)(36,37)(39,42)(43,44);(15,18)(16,20)(24,28)(26,29)(31,33)(35,37)(38,39,41,42)(40,43,45,44);(14,15,17,18)(16,19,20,21)(22,23)(24,26)(25,27)(28,29)(30,32,34,36)(31,35,33,37)(38,39)(40,44)(41,42)(43,45);(14,16)(15,19)(17,20)(18,21)(22,24)(23,26)(25,28)(27,29)(30,33,34,31)(32,35,36,37)(38,40,41,45)(39,43,42,44)

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, 10289);