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C2×C13×#2645 #15720957

order3328
nilpotency class2
isoclinismisoclinic class of #2613
automorphism?
homologyAbelianization (H1) = C25×C13 · Schur multiplier (H2) = C27

Aliases

direct productC2×C13×#2645

Subgroups

subgroupG/H
center, socle, prime radicalC24×C13C24
commutator, Frattini, cosocleC23C25×C13
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

1830 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 3328

A minimal faithful permutation representation — 5 generators on 39 points:

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

Conjugacy classes & character table

832 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 27606);