Finite Group Databasebeta

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D57×C11⋊C25 #44535451

order31350
automorphism?
homologyAbelianization (H1) = C2×C25 · Schur multiplier (H2) = C1

Aliases

direct productD57×C11⋊C25
unambiguous semidirect productC3⋊(D19×C11⋊C25)
unambiguous semidirect productC19⋊(D3×C11⋊C25)
unambiguous semidirect product(C11×D57)⋊C25

Splittings

derived, HallC3×C11×C19 ⋊ C2×C25
HallC3×C19×C11⋊C25 ⋊ C2
HallC19×C11⋊C25 ⋊ D3
HallC11×D57 ⋊ C25
HallC3×C11⋊C25 ⋊ D19
HallC11×C19 ⋊ D3×C25
HallC3×C19 ⋊ C2×C11⋊C25
HallC3×C11 ⋊ C25×D19
SylowC19 ⋊ D3×C11⋊C25
SylowC11 ⋊ C25×D57
SylowC3 ⋊ D19×C11⋊C25

Subgroups

subgroupG/H
center, Frattini, hypercenterC5C11⋊C5×D57
commutator, hypocenterC3×C11×C19C2×C25
Fitting, socle, cosocleC3×C5×C11×C19C2×C5
prime radicalC5×C11×D57C5
LCSG ▷ C3×C11×C19
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15675

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 24);