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C13⋊C3×D59 #17987180

order4602
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC13⋊C3×D59
unambiguous semidirect productC59⋊(C2×C13⋊C3)
unambiguous semidirect product(C13×D59)⋊C3

Splittings

Fitting, socle, derived, HallC13×C59 ⋊ C2×C3
HallC13⋊C3×C59 ⋊ C2
HallC13×D59 ⋊ C3
SylowC59 ⋊ C2×C13⋊C3
SylowC13 ⋊ C3×D59

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC13×C59C2×C3
LCSG ▷ C13×C59
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 72
transitive degreeμt(G) = 767

A minimal faithful permutation representation — 2 generators on 72 points:

(2,3,5)(4,7,10)(6,9,8)(11,13,12)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72);(1,2,4,3,6,10,7,11,13,5,8,12,9)(15,72)(16,71)(17,70)(18,69)(19,68)(20,67)(21,66)(22,65)(23,64)(24,63)(25,62)(26,61)(27,60)(28,59)(29,58)(30,57)(31,56)(32,55)(33,54)(34,53)(35,52)(36,51)(37,50)(38,49)(39,48)(40,47)(41,46)(42,45)(43,44)

Conjugacy classes & character table

217 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C13⋊C3×D59, C13⋊C3×D177, C5×C13⋊C3×D59, …
maximal normal subgroup ofC3×C13⋊C3×D59, C5×C13⋊C3×D59, C7×C13⋊C3×D59
maximal quotient ofC13⋊C9×D59, C3×C13⋊C3×D59, C13⋊C3×D177, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4602, 10);