C₁₃×#33564 #15719903

order	3328
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₃×#33564

Subgroups

	subgroup	G/H
center	C₄×C₁₃	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×Q₈	C₂⁴×C₁₃
socle	C₂×C₁₃	C₂×B(4,𝔽₂)
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#41 ◁ G

1112 conjugacy classes of subgroups; only the 218 normal subgroups are shown.

normal subgroups only

This group has 1112 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)(16,26)(17,23)(18,31)(19,22)(20,25)(21,27)(24,35)(28,42)(29,37)(30,40)(32,39)(33,41)(34,43)(36,44)(38,45);(14,16)(15,21)(17,27)(18,32)(19,34)(20,29)(22,36)(23,37)(24,38)(25,39)(26,31)(28,35)(30,45)(33,44)(40,43)(41,42);(15,22)(19,35)(21,36)(23,40)(24,25)(26,42)(28,34)(30,33)(31,41)(37,43)(38,39)(44,45);(14,17,20,18)(15,23,25,31)(16,27,29,32)(19,30,35,33)(21,37,39,26)(22,40,24,41)(28,44,34,45)(36,43,38,42)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 26552);