C₁₃×#33821 #15720160

order	3328
nilpotency class	4
isoclinism	isoclinic class of #33758
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#33821

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₂³×C₁₃	C₂×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

484 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 202 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)(15,18)(16,20)(22,23,28,32)(24,29,27,43)(25,35,38,52)(26,39,42,51)(30,45,47,37)(31,34,49,41)(33,50,36,48)(40,44,53,46);(14,15)(16,19)(17,18)(20,21)(22,24,28,27)(23,29,32,43)(25,36,38,33)(26,34,42,41)(30,46,47,44)(31,39,49,51)(35,48,52,50)(37,53,45,40);(15,18)(19,21)(22,25,28,38)(23,30,32,47)(24,33,27,36)(26,40,42,53)(29,44,43,46)(31,48,49,50)(34,45,41,37)(35,51,52,39);(14,16,17,20)(15,19,18,21)

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 26809);