Finite Group Databasebeta

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C13×#689 #11760137

order1040
isoclinismisoclinic class of #686
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×#689

Splittings

HallC5×C13 ⋊ Q16
SylowC5 ⋊ C13×Q16

Subgroups

subgroupG/H
centerC2×C13C22⋊D5
commutator, cosocleC4×C5C22×C13
FrattiniC4C2×D5×C13
FittingC5×Q8×C13C2
socle, prime radicalC2×C5×C13D4
hypercenterQ8×C13D5
hypocenterC5C13×Q16
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C13 ◁ C4×C13 ◁ Q8×C13

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 1040

A minimal faithful permutation representation — 2 generators on 34 points:

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

Conjugacy classes & character table

221 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1040, 66);