Finite Group Databasebeta

← Prev (#30628153) Next (#30628155) →

D7×C17×D33 #30628154

order15708
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2

Aliases

direct productD7×C17×D33
unambiguous semidirect product(C3×D7)⋊(C17×D11)
unambiguous semidirect product(C11×D7)⋊(D3×C17)

Splittings

Fitting, socle, HallC3×C7×C11×C17 ⋊ C22
derived, HallC3×C7×C11 ⋊ C22×C17
HallC7×C11×C17 ⋊ C2×D3
HallC3×C11×C17 ⋊ C2×D7
HallC3×C7×C17 ⋊ C2×D11
HallC11×C17 ⋊ D3×D7
HallC7×C17 ⋊ C2×D33
HallC7×C11 ⋊ C2×D3×C17
HallC3×C17 ⋊ D7×D11
HallC3×C11 ⋊ C2×D7×C17
HallC3×C7 ⋊ C2×C17×D11
SylowC11 ⋊ D3×D7×C17
SylowC7 ⋊ C2×C17×D33
SylowC3 ⋊ D7×C17×D11

Subgroups

subgroupG/H
center, hypercenterC17D7×D33
commutator, cosocle, hypocenterC3×C7×C11C22×C17
FrattiniC1G
Fitting, socleC3×C7×C11×C17C22
LCSG ▷ C3×C7×C11
UCSC1 ◁ C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3927

Conjugacy classes & character table

1530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 75);