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C2×C13×#2551 #15721263

order3328
nilpotency class2
isoclinismisoclinic class of #2403
automorphism?
homologyAbelianization (H1) = C25×C13 · Schur multiplier (H2) = C29

Aliases

direct productC2×C13×#2551

Subgroups

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

3182 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 3328

A minimal faithful permutation representation — 5 generators on 31 points:

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

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, 27912);