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C3×C5×D277⋊C3 #38735481

order24930
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×D277⋊C3
unambiguous semidirect productD277⋊(C32×C5)
unambiguous semidirect product(C277⋊C3)⋊(C2×C3×C5)
unambiguous semidirect product(C3×D277)⋊(C3×C5)
unambiguous semidirect product(C5×D277)⋊C32
unambiguous semidirect product(C3×C5×D277)⋊C3

Splittings

Fitting, socleC3×C5×C277 ⋊ C2×C3
derived, SylowC277 ⋊ C2×C32×C5
HallC3×C5×C277⋊C3 ⋊ C2
HallC5×D277 ⋊ C32
HallC3×C277⋊C3 ⋊ C2×C5
HallC5×C277 ⋊ C2×C32
HallD277 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC3×C5D277⋊C3
commutator, cosocle, hypocenterC277C2×C32×C5
FrattiniC1G
Fitting, socleC3×C5×C277C2×C3
LCSG ▷ C277
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4155

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24930, 14);