C₁₃×#29230 #15715569

order	3328
nilpotency class	3
isoclinism	isoclinic class of #24985
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#29230

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#555
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂×C₁₃	#2571
prime radical	C₂³×C₁₃	2₋¹⁺⁴
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

408 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 218 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 — 4 generators on 45 points:

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

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, 22218);