C₁₃×#11571 #15697910

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11549
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#11571

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₃
prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

350 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 102 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 — 3 generators on 45 points:

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

Conjugacy classes & character table

481 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 4559);