Finite Group Databasebeta

← Prev (#45682134) Next (#45682136) →

C157×D105 #45682135

order32970
automorphism?
homologyAbelianization (H1) = C2×C157 · Schur multiplier (H2) = C1

Aliases

direct productC157×D105
unambiguous semidirect productC3⋊(D35×C157)
unambiguous semidirect productC5⋊(D21×C157)
unambiguous semidirect productC7⋊(D15×C157)

Splittings

Fitting, socle, HallC3×C5×C7×C157 ⋊ C2
derived, HallC3×C5×C7 ⋊ C2×C157
HallC5×C7×C157 ⋊ D3
HallC3×C7×C157 ⋊ D5
HallC3×C5×C157 ⋊ D7
HallC7×C157 ⋊ D15
HallC5×C157 ⋊ D21
HallC3×C157 ⋊ D35
HallC5×C7 ⋊ D3×C157
HallC3×C7 ⋊ D5×C157
HallC3×C5 ⋊ D7×C157
SylowC7 ⋊ D15×C157
SylowC5 ⋊ D21×C157
SylowC3 ⋊ D35×C157

Subgroups

subgroupG/H
center, hypercenterC157D105
commutator, cosocle, hypocenterC3×C5×C7C2×C157
FrattiniC1G
Fitting, socleC3×C5×C7×C157C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C157

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16485

Conjugacy classes & character table

8478 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32970, 19);