C₁₃×#11752 #15698091

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11704
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#11752

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	C₂×SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

320 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 118 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 — 3 generators on 53 points:

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

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, 4740);