C₁₃×#21828 #15708167

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×#21828

Subgroups

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

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

normal subgroups only

This group has 990 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) = 832

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

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, 14816);