C₁₃×#23928 #15710267

order	3328
nilpotency class	3
isoclinism	isoclinic class of #23924
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₁₃×#23928

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₁₃×#41 ◁ G

1696 conjugacy classes of subgroups; only the 302 normal subgroups are shown.

normal subgroups only

This group has 1696 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) = 53
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 4 generators on 53 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(22,23,27,31)(24,28,33,42)(25,35,37,45)(26,38,40,30)(29,39,44,36)(32,46,47,53)(34,50,49,43)(41,51,52,48);(15,17)(18,19)(20,21)(22,24,27,33)(23,28,31,42)(25,32,37,47)(26,34,40,49)(29,41,44,52)(30,43,38,50)(35,46,45,53)(36,48,39,51);(19,21)(22,25,27,37)(23,29,31,44)(24,32,33,47)(26,39,40,36)(28,41,42,52)(30,45,38,35)(34,51,49,48)(43,53,50,46);(15,17)(24,33)(28,42)(32,47)(34,49)(41,52)(43,50)(46,53)(48,51)

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, 16916);