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C5⋊((C43⋊C3)⋊D19) #37587798

order24510
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC5⋊((C43⋊C3)⋊D19)
unambiguous semidirect product(C43⋊C3)⋊D95

Splittings

Fitting, socle, derived, HallC5×C19×C43 ⋊ C2×C3
HallC5×C19×C43⋊C3 ⋊ C2
HallD4085 ⋊ C3
HallC19×C43⋊C3 ⋊ D5
HallC19×C43 ⋊ C3×D5
HallC5×C43⋊C3 ⋊ D19
HallC5×C43 ⋊ C3×D19
HallC43⋊C3 ⋊ D95
HallC5×C19 ⋊ D43⋊C3
SylowC43 ⋊ C3×D95
SylowC19 ⋊ C5⋊(D43⋊C3)
SylowC5 ⋊ (C43⋊C3)⋊D19

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C19×C43C2×C3
LCSG ▷ C5×C19×C43
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 67
transitive degreeμt(G) = 4085

A minimal faithful permutation representation — 2 generators on 67 points:

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

Polycyclic presentation:

2,3,5,19,43|c^a=c^4,d^a=d^18,e^a=e^42,e^b=e^36

Conjugacy classes & character table

812 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24510, 45);