C₁₃×#9516 #15695855

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9495
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#9516

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#386
commutator	C₂⁴	C₂²×C₄×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₂×C₁₃×#120	C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

626 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 122 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) = 416

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

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

Conjugacy classes & character table

481 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 2504);