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D17×D231 #30628145

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

Aliases

direct productD17×D231
unambiguous semidirect product(C3×D17)⋊D77
unambiguous semidirect product(C7×D17)⋊D33
unambiguous semidirect product(C11×D17)⋊D21

Splittings

Fitting, socle, derived, HallC3×C7×C11×C17 ⋊ C22
HallC7×C11×C17 ⋊ C2×D3
HallC3×C11×C17 ⋊ C2×D7
HallC3×C7×C17 ⋊ C2×D11
HallC3×C7×C11 ⋊ C2×D17
HallC11×C17 ⋊ C2×D21
HallC7×C17 ⋊ C2×D33
HallC7×C11 ⋊ D3×D17
HallC3×C17 ⋊ C2×D77
HallC3×C11 ⋊ D7×D17
HallC3×C7 ⋊ D11×D17
SylowC17 ⋊ C2×D231
SylowC11 ⋊ D17×D21
SylowC7 ⋊ D17×D33
SylowC3 ⋊ D17×D77

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C17C22
LCSG ▷ C3×C7×C11×C17
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3927

Conjugacy classes & character table

1170 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 66);