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C13⋊(D101⋊C5) #27190055

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

Aliases

unambiguous semidirect productC13⋊(D101⋊C5)
unambiguous semidirect product(C101⋊C5)⋊D13
unambiguous semidirect productD1313⋊C5

Splittings

Fitting, socle, derived, HallC13×C101 ⋊ C2×C5
HallC13×C101⋊C5 ⋊ C2
HallD1313 ⋊ C5
HallC101⋊C5 ⋊ D13
SylowC101 ⋊ C5×D13
SylowC13 ⋊ D101⋊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:

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

Polycyclic presentation:

2,5,13,101|c^a=c^12,d^a=d^100,d^b=d^95

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#19126824⋊C5, #19126825⋊C5, D13×D101⋊C5, …
maximal normal subgroup of#19126824⋊C5, #19126825⋊C5, D13×D101⋊C5, …
maximal quotient ofDic1313⋊C5, C2×C13⋊(D101⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13130, 12);