Finite Group Databasebeta

← Prev (#38788438) Next (#38788440) →

C3×C17×C101⋊C5 #38788439

order25755
automorphism?
homologyAbelianization (H1) = C3×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×C101⋊C5
unambiguous semidirect productC101⋊(C3×C5×C17)
unambiguous semidirect product(C3×C101)⋊(C5×C17)
unambiguous semidirect product(C17×C101)⋊(C3×C5)
unambiguous semidirect product(C3×C17×C101)⋊C5

Splittings

Fitting, socle, HallC3×C17×C101 ⋊ C5
derived, SylowC101 ⋊ C3×C5×C17
HallC17×C101 ⋊ C3×C5
HallC3×C101 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC3×C17C101⋊C5
commutator, cosocle, hypocenterC101C3×C5×C17
FrattiniC1G
Fitting, socleC3×C17×C101C5
LCSG ▷ C101
UCSC1 ◁ C3×C17

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5151

Conjugacy classes & character table

1275 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25755, 2);