Finite Group Databasebeta

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D11×C25×C19⋊C3 #44535455

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productD11×C25×C19⋊C3
unambiguous semidirect product(C19×D11×C25)⋊C3

Splittings

Fitting, HallC11×C19×C25 ⋊ C2×C3
derived, HallC11×C19 ⋊ C2×C3×C25
HallC11×C25×C19⋊C3 ⋊ C2
HallC19×D11×C25 ⋊ C3
HallC11×C19⋊C3 ⋊ C2×C25
HallC19×C25 ⋊ C3×D11
HallC19×D11 ⋊ C3×C25
HallC11×C25 ⋊ C2×C19⋊C3
SylowC19 ⋊ C3×D11×C25
SylowC11 ⋊ C2×C25×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC25D11×C19⋊C3
commutator, hypocenterC11×C19C2×C3×C25
FrattiniC5C5×D11×C19⋊C3
FittingC11×C19×C25C2×C3
socle, cosocleC5×C11×C19C2×C3×C5
prime radicalC5×D11×C19⋊C3C5
LCSG ▷ C11×C19
UCSC1 ◁ C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5225

Conjugacy classes & character table

1575 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 28);