Finite Group Databasebeta

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C3×C11⋊C5×D115 #49182121

order37950
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊C5×D115
unambiguous semidirect productC5⋊(C3×D23×C11⋊C5)
unambiguous semidirect productC23⋊(C3×D5×C11⋊C5)
unambiguous semidirect product(C11×D115)⋊(C3×C5)
unambiguous semidirect product(C3×C11×D115)⋊C5

Splittings

Fitting, socleC3×C5×C11×C23 ⋊ C2×C5
derivedC5×C11×C23 ⋊ C2×C3×C5
HallC3×C5×C23×C11⋊C5 ⋊ C2
HallC5×C23×C11⋊C5 ⋊ C2×C3
HallC3×C5×C11⋊C5 ⋊ D23
HallC3×C11×C23 ⋊ C5×D5
HallC5×C11⋊C5 ⋊ C3×D23
HallC11×C23 ⋊ C3×C5×D5
HallC3×C23 ⋊ D5×C11⋊C5
HallC3×C11 ⋊ C5×D115
SylowC23 ⋊ C3×D5×C11⋊C5
SylowC11 ⋊ C3×C5×D115

Subgroups

subgroupG/H
center, hypercenterC3C11⋊C5×D115
commutator, cosocle, hypocenterC5×C11×C23C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C23C2×C5
LCSG ▷ C5×C11×C23
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3795

Conjugacy classes & character table

1239 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 58);