Finite Group Databasebeta

← Prev (#38736001) Next (#38736003) →

C3⋊(C5⋊(C7⋊D119)) #38736002

order24990
automorphism?
homologyAbelianization (H1) = C2 · Schur multiplier (H2) = C7

Aliases

unambiguous semidirect productC3⋊(C5⋊(C7⋊D119))
unambiguous semidirect productC5⋊(C3⋊(C7⋊D119))
unambiguous semidirect productC7⋊D1785
unambiguous semidirect productC17⋊(C3⋊(C5⋊(C7⋊D7)))

Splittings

Fitting, socle, derived, HallC3×C5×C72×C17 ⋊ C2
HallC5×C72×C17 ⋊ D3
HallC3×C72×C17 ⋊ D5
HallC72×C17 ⋊ D15
HallC3×C5×C72 ⋊ D17
HallC3×C5×C17 ⋊ C7⋊D7
HallC5×C72 ⋊ D51
HallC3×C72 ⋊ D85
HallC5×C17 ⋊ C3⋊(C7⋊D7)
HallC3×C17 ⋊ C5⋊(C7⋊D7)
SylowC72 ⋊ D255
SylowC17 ⋊ C3⋊(C5⋊(C7⋊D7))
HallC3×C5 ⋊ C7⋊D119
SylowC5 ⋊ C3⋊(C7⋊D119)
SylowC3 ⋊ C5⋊(C7⋊D119)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C72×C17C2
LCSG ▷ C3×C5×C72×C17
UCSC1

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12495

Polycyclic presentation:

2,3,5,7^2,17|b^a=b^2,c^a=c^4,d^a=d^6,e^a=e^6,f^a=f^16

Conjugacy classes & character table

6249 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 92);