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C22×C33⋊C13 #13064045

order1404
isoclinismisoclinic class of C33⋊C13
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productC22×C33⋊C13
unambiguous semidirect product(C22×C33)⋊C13

Splittings

Fitting, socle, HallC22×C33 ⋊ C13
derived, SylowC33 ⋊ C22×C13

Subgroups

subgroupG/H
center, hypercenterC22C33⋊C13
commutator, cosocle, hypocenterC33C22×C13
FrattiniC1G
Fitting, socleC22×C33C13
LCSG ▷ C33
UCSC1 ◁ C22

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 108

A minimal faithful permutation representation — 2 generators on 31 points:

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1404, 177);