Finite Group Databasebeta

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D19×D231 #31798305

order17556
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD19×D231
unambiguous semidirect product(C3×D19)⋊D77
unambiguous semidirect product(C7×D19)⋊D33
unambiguous semidirect product(C11×D19)⋊D21

Splittings

Fitting, socle, derived, HallC3×C7×C11×C19 ⋊ C22
HallC7×C11×C19 ⋊ C2×D3
HallC3×C11×C19 ⋊ C2×D7
HallC3×C7×C19 ⋊ C2×D11
HallC3×C7×C11 ⋊ C2×D19
HallC11×C19 ⋊ C2×D21
HallC7×C19 ⋊ C2×D33
HallC7×C11 ⋊ D3×D19
HallC3×C19 ⋊ C2×D77
HallC3×C11 ⋊ D7×D19
HallC3×C7 ⋊ D11×D19
SylowC19 ⋊ C2×D231
SylowC11 ⋊ D19×D21
SylowC7 ⋊ D19×D33
SylowC3 ⋊ D19×D77

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C7×C11×C19C22
LCSG ▷ C3×C7×C11×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4389

Conjugacy classes & character table

1287 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 120);