Finite Group Databasebeta

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C52×C11×D57 #44535533

order31350
automorphism?
homologyAbelianization (H1) = C2×C52×C11 · Schur multiplier (H2) = C5

Aliases

direct productC52×C11×D57
unambiguous semidirect productC3⋊(C52×C11×D19)
unambiguous semidirect productC19⋊(C52×D3×C11)

Splittings

Fitting, socle, HallC3×C52×C11×C19 ⋊ C2
derived, HallC3×C19 ⋊ C2×C52×C11
HallC52×C11×C19 ⋊ D3
HallC3×C52×C19 ⋊ C2×C11
HallC3×C52×C11 ⋊ D19
HallC3×C11×C19 ⋊ C2×C52
HallC52×C19 ⋊ D3×C11
HallC11×C19 ⋊ C52×D3
HallC3×C52 ⋊ C11×D19
HallC3×C11 ⋊ C52×D19
SylowC19 ⋊ C52×D3×C11
SylowC3 ⋊ C52×C11×D19

Subgroups

subgroupG/H
center, hypercenterC52×C11D57
commutator, cosocle, hypocenterC3×C19C2×C52×C11
FrattiniC1G
Fitting, socleC3×C52×C11×C19C2
LCSG ▷ C3×C19
UCSC1 ◁ C52×C11

128 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, 106);