Finite Group Databasebeta

← Prev (#27190053) Next (#27190055) →

D13×C101⋊C5 #27190054

order13130
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C1

Aliases

direct productD13×C101⋊C5
unambiguous semidirect productC13⋊(C2×C101⋊C5)
unambiguous semidirect product(D13×C101)⋊C5

Splittings

Fitting, socle, derived, HallC13×C101 ⋊ C2×C5
HallC13×C101⋊C5 ⋊ C2
HallD13×C101 ⋊ C5
SylowC101 ⋊ C5×D13
SylowC13 ⋊ C2×C101⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C101C2×C5
LCSG ▷ C13×C101
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 114
transitive degreeμt(G) = 1313

A minimal faithful permutation representation — 2 generators on 114 points:

(2,3,5,9,17)(4,7,13,25,45)(6,11,21,37,31)(8,15,28,50,79)(10,19,33,18,32)(12,23,41,66,72)(14,26,47,74,54)(16,29,51,80,65)(20,35,58,46,73)(22,39,30,52,55)(24,43,69,93,98)(27,48,76,36,60)(34,57,38,62,56)(40,64,87,90,95)(42,67,49,77,82)(44,70,94,101,89)(53,81,84,63,71)(59,85,75,96,83)(61,86,68,91,92)(78,97,99,88,100)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114);(1,2,4,8,16,30,53,28,47,75,64,88,70,57,84,99,39,63,43,33,56,83,21,38,23,42,68,92,101,94,11,22,40,65,89,100,5,10,20,36,61,87,93,51,76,80,91,96,97,85,79,98,67,74,77,58,66,90,41,50,48,73,95,86,62,81,26,45,72,60,37,52,13,25,46,35,59,29,32,55,82,19,34,15,17,31,54,9,18,7,14,27,49,78,69,3,6,12,24,44,71)(102,103,105,107,109,111,113,114,112,110,108,106,104)

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#19126826⋊C5, #261×C101⋊C5, D13×D101⋊C5, …
maximal normal subgroup of#19126826⋊C5, #261×C101⋊C5, D13×D101⋊C5, …
maximal quotient ofDic13×C101⋊C5, C2×D13×C101⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13130, 11);