Finite Group Databasebeta

← Prev (#31775521) Next (#31775523) →

C5×Dic3×C97⋊C3 #31775522

order17460
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic3×C97⋊C3
unambiguous semidirect productC3⋊(C4×C5×C97⋊C3)
unambiguous semidirect product(Dic3×C97)⋊(C3×C5)
unambiguous semidirect product(C5×Dic3×C97)⋊C3

Splittings

derivedC3×C97 ⋊ C3×C4×C5
HallC3×C5×C97⋊C3 ⋊ C4
HallC3×C97⋊C3 ⋊ C4×C5
HallC5×C97 ⋊ C3×Dic3
SylowC97 ⋊ C3×C5×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C5D3×C97⋊C3
commutator, hypocenterC3×C97C3×C4×C5
FrattiniC2C5×D3×C97⋊C3
Fitting, socleC2×C3×C5×C97C2×C3
prime radicalC2×C3×C5×C97⋊C3C2
cosocleC2×C3×C97C2×C3×C5
LCSG ▷ C3×C97
UCSC1 ◁ C2×C5

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5820

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17460, 58);