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C5×D3×D61⋊C5 #32913007

order18300
automorphism?
homologyAbelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC5×D3×D61⋊C5
unambiguous semidirect productD61⋊(C52×D3)
unambiguous semidirect product(D3×D61)⋊C52
unambiguous semidirect product(C3×D61⋊C5)⋊(C2×C5)
unambiguous semidirect product(D3×C61⋊C5)⋊(C2×C5)
unambiguous semidirect product(C3⋊(D61⋊C5))⋊(C2×C5)
unambiguous semidirect product(C5×D3×D61)⋊C5

Splittings

Fitting, socleC3×C5×C61 ⋊ C22×C5
derived, HallC3×C61 ⋊ C22×C52
HallC3×C5×C61⋊C5 ⋊ C22
HallC5×C61⋊C5 ⋊ C2×D3
HallD3×D61 ⋊ C52
SylowC61 ⋊ C2×C52×D3
SylowC3 ⋊ C2×C5×D61⋊C5

Subgroups

subgroupG/H
center, hypercenterC5D3×D61⋊C5
commutator, cosocle, hypocenterC3×C61C22×C52
FrattiniC1G
Fitting, socleC3×C5×C61C22×C5
LCSG ▷ C3×C61
UCSC1 ◁ C5

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 915

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18300, 130);