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C2×C3⋊(C5⋊(D61⋊C5)) #32913071

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

Aliases

direct productC2×C3⋊(C5⋊(D61⋊C5))
unambiguous semidirect product(C2×C3)⋊(C5⋊(D61⋊C5))
unambiguous semidirect product(C2×C5)⋊(C3⋊(D61⋊C5))
unambiguous semidirect product(C2×C61⋊C5)⋊D15
unambiguous semidirect product(C2×D915)⋊C5

Splittings

Fitting, socleC2×C3×C5×C61 ⋊ C2×C5
derivedC3×C5×C61 ⋊ C22×C5
HallC3×C5×C61⋊C5 ⋊ C22
HallC5×C61⋊C5 ⋊ C2×D3
HallC3×C61 ⋊ C2×C5×D5
SylowC61 ⋊ C2×C5×D15
SylowC3 ⋊ C2×C5⋊(D61⋊C5)

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C5⋊(D61⋊C5))
commutator, cosocle, hypocenterC3×C5×C61C22×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C61C2×C5
LCSG ▷ C3×C5×C61
UCSC1 ◁ C2

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1830

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18300, 194);