C₁₃×#12070 #15698409

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

Aliases

direct product

C₁₃×#12070

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₄×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₄×D₈
prime radical	C₂×C₁₃×D₈	C₂×C₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₄×C₈×C₁₃ ◁ C₈²×C₁₃ ◁ G

226 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 37
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16,18,19,21,20)(22,23,25,29)(24,27,33,35)(26,34,32,30)(28,37,36,31);(23,27)(24,31)(26,32)(28,30)(29,35)(33,37)(34,36);(14,16,17,19,18,20,21,15)

Conjugacy classes & character table

754 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5058);