C₁₃×#11770 #15698109

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11769
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#11770

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1505
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₃
prime radical	C₁₃×#3176	C₂
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

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

normal subgroups only

This group has 316 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)(16,21)(17,30,32,20)(18,23)(19,25)(22,31,34,41)(24,27)(26,36)(28,42,43,33)(29,38)(35,39,44,45)(37,40);(15,20)(16,26)(17,31)(18,27)(21,35)(22,24)(23,34)(25,30)(28,43)(29,40)(32,41)(33,36)(37,42)(38,44);(14,16,27,40,19,29,18,26)(15,21,24,37,25,38,23,36)(17,28,41,45,32,43,31,39)(20,33,34,44,30,42,22,35)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 4758);