C₁₃×#7109 #15693448

order	3328
nilpotency class	4
isoclinism	isoclinic class of #1339
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#7109

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#327
commutator	C₂×C₈	C₂×C₈×C₁₃
Frattini, cosocle	C₂×#97	C₂²×C₁₃
socle	C₂×C₁₃	#1270
prime radical	C₂×C₁₃×#135	C₄
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

228 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 70 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 — 2 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,24,26,40,28,41,27,36)(17,29,32,21)(18,23)(19,22)(20,25,34,30,35,42,39,43)(31,37)(33,44,45,38);(14,16)(15,20)(17,30)(18,26)(19,28)(21,36)(22,35)(23,39)(24,38)(25,33)(27,31)(29,40)(32,43)(34,37)(41,44)(42,45)

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, 97);