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C22×C13⋊C27 #13063880

order1404
isoclinismisoclinic class of C13⋊C3
automorphism?
homologyAbelianization (H1) = C22×C27 · Schur multiplier (H2) = C2

Aliases

direct productC22×C13⋊C27

Splittings

derived, SylowC13 ⋊ C22×C27
HallC22×C13 ⋊ C27

Subgroups

subgroupG/H
center, hypercenterC22×C9C13⋊C3
commutator, hypocenterC13C22×C27
FrattiniC9C22×C13⋊C3
FittingC22×C9×C13C3
socle, prime radicalC22×C3×C13C9
cosocleC9×C13C22×C3
LCSG ▷ C13
UCSC1 ◁ C22×C9

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 44
transitive degreeμt(G) = 1404

A minimal faithful permutation representation — 2 generators on 44 points:

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

Conjugacy classes & character table

252 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1404, 12);