C₁₃×#33825 #15720164

order	3328
nilpotency class	4
isoclinism	isoclinic class of #33764
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#33825

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₁₃×#117 ◁ C₁₃×#405 ◁ G

512 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 194 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)(24,28)(25,29)(26,39)(27,32)(30,36)(31,37)(33,41)(34,40)(35,49)(38,45)(42,48)(43,47)(44,50)(46,51)(52,53);(14,15)(16,19)(17,18)(20,21)(22,24,27,33)(23,28,32,41)(25,34,38,46)(26,35,37,47)(29,40,45,51)(30,42,44,52)(31,43,39,49)(36,48,50,53);(15,18)(19,21)(23,29)(25,36)(26,37)(28,40)(30,31)(32,45)(34,48)(35,47)(38,50)(39,44)(41,51)(42,43)(46,53)(49,52);(14,16,17,20)(15,19,18,21)(24,33)(28,41)(34,46)(35,47)(40,51)(42,52)(43,49)(48,53)

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, 26813);