C₁₃×#62694 #15749033

order	3328
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₃ · Schur multiplier (H₂) = C₂¹³

Aliases

direct product

C₁₃×#62694

Subgroups

	subgroup	G/H
center	C₄²×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
socle	C₂²×C₁₃	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₁₃ ◁ G

6640 conjugacy classes of subgroups; only the 5670 normal subgroups are shown.

normal subgroups only

This group has 6640 conjugacy classes of subgroups — too many to draw. Only its 5670 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 — 6 generators on 45 points:

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

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 55682);