Finite Group Databasebeta

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C52⋊C3×D209 #44535493

order31350
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C5

Aliases

direct productC52⋊C3×D209
unambiguous semidirect productC11⋊(D19×C52⋊C3)

Splittings

Fitting, socle, derived, HallC52×C11×C19 ⋊ C2×C3
HallC11×C19×C52⋊C3 ⋊ C2
HallC52×D209 ⋊ C3
HallC19×C52⋊C3 ⋊ D11
HallC11×C52⋊C3 ⋊ D19
HallC52×C19 ⋊ C3×D11
HallC52×C11 ⋊ C3×D19
HallC11×C19 ⋊ C2×C52⋊C3
SylowC52 ⋊ C3×D209
SylowC19 ⋊ D11×C52⋊C3
SylowC11 ⋊ D19×C52⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC52×C11×C19C2×C3
LCSG ▷ C52×C11×C19
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

1166 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 66);