C₁₃×#10040 #15696379

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10038
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10040

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₁₃×#3214	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

500 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 1664

A minimal faithful permutation representation — 3 generators on 45 points:

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

Conjugacy classes & character table

403 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3028);