C₁₃×#13351 #15699690

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13350
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#13351

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2021
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₃
prime radical	C₁₃×#3027	C₂
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#41 ◁ G

710 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 94 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 — 3 generators on 45 points:

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

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6339);