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C5×C103⋊C3 #13095403

order1545
isoclinismisoclinic class of C103⋊C3
automorphism?
homologyAbelianization (H1) = C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C103⋊C3
unambiguous semidirect productC103⋊(C3×C5)
unambiguous semidirect product(C5×C103)⋊C3

Splittings

Fitting, socle, HallC5×C103 ⋊ C3
derived, SylowC103 ⋊ C3×C5

Subgroups

subgroupG/H
center, hypercenterC5C103⋊C3
commutator, cosocle, hypocenterC103C3×C5
FrattiniC1G
Fitting, socleC5×C103C3
LCSG ▷ C103
UCSC1 ◁ C5

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 108
transitive degreeμt(G) = 515

A minimal faithful permutation representation — 2 generators on 108 points:

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

Conjugacy classes & character table

185 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×C103⋊C3, C5×D103⋊C3, D5×C103⋊C3, …
maximal normal subgroup ofC2×C5×C103⋊C3, C5×D103⋊C3, D5×C103⋊C3, …
maximal quotient ofC2×C5×C103⋊C3, C5×C103⋊C9, C3×C5×C103⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1545, 1);