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C5×C33⋊C13 #13182179

order1755
isoclinismisoclinic class of C33⋊C13
automorphism?
homologyAbelianization (H1) = C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C33⋊C13
unambiguous semidirect productC33⋊(C5×C13)
unambiguous semidirect product(C33×C5)⋊C13

Splittings

Fitting, socle, HallC33×C5 ⋊ C13
derived, SylowC33 ⋊ C5×C13

Subgroups

subgroupG/H
center, hypercenterC5C33⋊C13
commutator, cosocle, hypocenterC33C5×C13
FrattiniC1G
Fitting, socleC33×C5C13
LCSG ▷ C33
UCSC1 ◁ C5

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 135

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

75 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1755, 12);