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(C43⋊C3)⋊D91 #37553531

order23478
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C43⋊C3)⋊D91

Splittings

Fitting, socle, derived, HallC7×C13×C43 ⋊ C2×C3
HallC7×C13×C43⋊C3 ⋊ C2
HallD3913 ⋊ C3
HallC13×C43⋊C3 ⋊ D7
HallC7×C43⋊C3 ⋊ D13
HallC13×C43 ⋊ C3×D7
HallC7×C43 ⋊ C3×D13
HallC43⋊C3 ⋊ D91
HallC7×C13 ⋊ D43⋊C3
SylowC43 ⋊ C3×D91
SylowC13 ⋊ (C43⋊C3)⋊D7
SylowC7 ⋊ (C43⋊C3)⋊D13

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C13×C43C2×C3
LCSG ▷ C7×C13×C43
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 63
transitive degreeμt(G) = 3913

A minimal faithful permutation representation — 2 generators on 63 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)(58,59)(60,61)(62,63);(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)(44,45,47,49,51,53,55,56,54,52,50,48,46)(57,58,60,62,63,61,59)

Polycyclic presentation:

2,3,7,13,43|c^a=c^6,d^a=d^12,e^a=e^42,e^b=e^36

Conjugacy classes & character table

778 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23478, 120);