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C5⋊(C17⋊(D73⋊C3)) #49151925

order37230
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC5⋊(C17⋊(D73⋊C3))
unambiguous semidirect productC17⋊(C5⋊(D73⋊C3))
unambiguous semidirect product(C73⋊C3)⋊D85
unambiguous semidirect productD6205⋊C3

Splittings

Fitting, socle, derived, HallC5×C17×C73 ⋊ C2×C3
HallC5×C17×C73⋊C3 ⋊ C2
HallD6205 ⋊ C3
HallC17×C73⋊C3 ⋊ D5
HallC17×C73 ⋊ C3×D5
HallC5×C73⋊C3 ⋊ D17
HallC5×C73 ⋊ C3×D17
HallC73⋊C3 ⋊ D85
HallC5×C17 ⋊ D73⋊C3
SylowC73 ⋊ C3×D85
SylowC17 ⋊ C5⋊(D73⋊C3)
SylowC5 ⋊ C17⋊(D73⋊C3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C17×C73C2×C3
LCSG ▷ C5×C17×C73
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 95
transitive degreeμt(G) = 6205

A minimal faithful permutation representation — 2 generators on 95 points:

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

Polycyclic presentation:

2,3,5,17,73|c^a=c^4,d^a=d^16,e^a=e^72,e^b=e^8

Conjugacy classes & character table

1152 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37230, 24);