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C11⋊C5×D345 #49182129

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

Aliases

direct productC11⋊C5×D345
unambiguous semidirect productC3⋊(C11⋊C5×D115)
unambiguous semidirect productC5⋊(C11⋊C5×D69)
unambiguous semidirect productC23⋊(D15×C11⋊C5)
unambiguous semidirect product(C11×D345)⋊C5

Splittings

Fitting, socle, derivedC3×C5×C11×C23 ⋊ C2×C5
HallC3×C5×C23×C11⋊C5 ⋊ C2
HallC5×C23×C11⋊C5 ⋊ D3
HallC3×C5×C11⋊C5 ⋊ D23
HallC3×C11×C23 ⋊ C5×D5
HallC5×C11⋊C5 ⋊ D69
HallC11×C23 ⋊ C5×D15
HallC3×C23 ⋊ D5×C11⋊C5
HallC3×C11 ⋊ C5×D115
SylowC23 ⋊ D15×C11⋊C5
SylowC11 ⋊ C5×D345
SylowC3 ⋊ C11⋊C5×D115

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C23C2×C5
LCSG ▷ C3×C5×C11×C23
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3795

Conjugacy classes & character table

1218 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 66);