Finite Group Databasebeta

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C11×C25×D57 #44535440

order31350
automorphism?
homologyAbelianization (H1) = C2×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC11×C25×D57
unambiguous semidirect productC3⋊(C11×C25×D19)
unambiguous semidirect productC19⋊(D3×C11×C25)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC11×C25D57
commutator, hypocenterC3×C19C2×C11×C25
FrattiniC5C5×C11×D57
FittingC3×C11×C19×C25C2
socleC3×C5×C11×C19C2×C5
prime radicalC5×C11×D57C5
cosocleC3×C5×C19C2×C5×C11
LCSG ▷ C3×C19
UCSC1 ◁ C11×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15675

Conjugacy classes & character table

8250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 13);