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C59⋊#64424 #31774754

order17346
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC59⋊#64424

Splittings

Fitting, socle, derived, HallC72×C59 ⋊ C2×C3
HallC59×#3861 ⋊ C2
HallC7⋊D413 ⋊ C3
Hall#3861 ⋊ D59
SylowC59 ⋊ #64424
SylowC72 ⋊ C3×D59

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC72×C59C2×C3
LCSG ▷ C72×C59
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 73
transitive degreeμt(G) = 2891

A minimal faithful permutation representation — 3 generators on 73 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(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)(61,64,65,62,63,66)(68,71,72,69,70,73);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(67,68,70,73,72,71,69);(60,61,63,66,65,64,62)

Polycyclic presentation:

2,3,7^2,59|c^a=c^6,d^a=d^6,e^a=e^58,c^b=c^2,d^b=d^2

Conjugacy classes & character table

565 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD59×#64424, #64423⋊D59, C2×C59⋊#64424
maximal normal subgroup ofD59×#64424, #64423⋊D59, C2×C59⋊#64424
maximal quotient ofC59⋊#10596874, C2×C59⋊#64424

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17346, 18);