C₁₃×#21827 #15708166

order	3328
nilpotency class	3
isoclinism	isoclinic class of #17405
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₃×#21827

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×C₂²⋊C₄
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₁₃×C₂²⋊C₄ ◁ G

1130 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 366 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 — 4 generators on 45 points:

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

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 14815);