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C5×C3⋊(D277⋊C3) #38735484

order24930
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊(D277⋊C3)
unambiguous semidirect productC3⋊(C5×D277⋊C3)
unambiguous semidirect product(C277⋊C3)⋊(C5×D3)
unambiguous semidirect productD831⋊(C3×C5)
unambiguous semidirect product(C5×D831)⋊C3

Splittings

Fitting, socleC3×C5×C277 ⋊ C2×C3
derivedC3×C277 ⋊ C2×C3×C5
HallC3×C5×C277⋊C3 ⋊ C2
HallC3×C277⋊C3 ⋊ C2×C5
HallC5×C277 ⋊ C3×D3
SylowC277 ⋊ C3×C5×D3

Subgroups

subgroupG/H
center, hypercenterC5C3⋊(D277⋊C3)
commutator, cosocle, hypocenterC3×C277C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C277C2×C3
LCSG ▷ C3×C277
UCSC1 ◁ C5

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4155

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24930, 17);