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C3×C5×D23×C11⋊C5 #49182117

order37950
automorphism?
homologyAbelianization (H1) = C2×C3×C52 · Schur multiplier (H2) = C5

Aliases

direct productC3×C5×D23×C11⋊C5
unambiguous semidirect productC23⋊(C2×C3×C5×C11⋊C5)
unambiguous semidirect product(C11×D23)⋊(C3×C52)
unambiguous semidirect product(C3×C11×D23)⋊C52
unambiguous semidirect product(C5×C11×D23)⋊(C3×C5)
unambiguous semidirect product(C3×C5×C11×D23)⋊C5

Splittings

Fitting, socleC3×C5×C11×C23 ⋊ C2×C5
derived, HallC11×C23 ⋊ C2×C3×C52
HallC3×C5×C23×C11⋊C5 ⋊ C2
HallC5×C23×C11⋊C5 ⋊ C2×C3
HallC3×C11×D23 ⋊ C52
HallC3×C11×C23 ⋊ C2×C52
HallC11×D23 ⋊ C3×C52
HallC3×C23 ⋊ C2×C5×C11⋊C5
HallC3×C11 ⋊ C52×D23
SylowC23 ⋊ C2×C3×C5×C11⋊C5
SylowC11 ⋊ C3×C52×D23

Subgroups

subgroupG/H
center, hypercenterC3×C5D23×C11⋊C5
commutator, cosocle, hypocenterC11×C23C2×C3×C52
FrattiniC1G
Fitting, socleC3×C5×C11×C23C2×C5
LCSG ▷ C11×C23
UCSC1 ◁ C3×C5

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3795

Conjugacy classes & character table

1365 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37950, 54);