C₁₃×#12485 #15698824

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12483
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₃×#12485

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#459
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₃
prime radical	C₁₃×#2206	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ C₈²×C₁₃ ◁ G

248 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 78 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)(15,18)(16,20)(19,21)(22,23)(24,27)(25,28)(26,34)(29,33)(30,32)(31,35)(36,37);(14,15,16,18,17,19,20,21)(23,27)(28,35)(29,36)(30,34);(15,19)(18,21)(23,28)(25,33)(26,32)(27,35)(29,30)(31,37)(34,36)

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, 5473);