Finite Group Databasebeta

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C3×C19×C5⋊D55 #44535530

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C5

Aliases

direct productC3×C19×C5⋊D55
unambiguous semidirect productC5⋊(C3×C19×D55)
unambiguous semidirect productC11⋊(C3×C19×C5⋊D5)

Splittings

Fitting, socle, HallC3×C52×C11×C19 ⋊ C2
derived, HallC52×C11 ⋊ C2×C3×C19
HallC52×C11×C19 ⋊ C2×C3
HallC3×C52×C19 ⋊ D11
HallC3×C52×C11 ⋊ C2×C19
HallC3×C11×C19 ⋊ C5⋊D5
HallC52×C19 ⋊ C3×D11
HallC11×C19 ⋊ C3×C5⋊D5
HallC3×C52 ⋊ C19×D11
HallC3×C11 ⋊ C19×C5⋊D5
SylowC52 ⋊ C3×C19×D11
SylowC11 ⋊ C3×C19×C5⋊D5

Subgroups

subgroupG/H
center, hypercenterC3×C19C5⋊D55
commutator, cosocle, hypocenterC52×C11C2×C3×C19
FrattiniC1G
Fitting, socleC3×C52×C11×C19C2
LCSG ▷ C52×C11
UCSC1 ◁ C3×C19

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15675

Conjugacy classes & character table

7923 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 103);