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C2×C5×D1635 #45658378

order32700
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D1635
unambiguous semidirect product(C2×C3)⋊(C5×D545)
unambiguous semidirect product(C2×C5)⋊(C5×D327)
unambiguous semidirect product(C2×C109)⋊(C5×D15)

Splittings

Fitting, socleC2×C3×C52×C109 ⋊ C2
derivedC3×C5×C109 ⋊ C22×C5
HallC3×C52×C109 ⋊ C22
HallC52×C109 ⋊ C2×D3
HallC3×C109 ⋊ C2×C5×D5
SylowC109 ⋊ C2×C5×D15
HallC3×C52 ⋊ C2×D109
SylowC52 ⋊ C2×D327
SylowC3 ⋊ C2×C5×D545

Subgroups

subgroupG/H
center, hypercenterC2×C5D1635
commutator, cosocle, hypocenterC3×C5×C109C22×C5
FrattiniC1G
Fitting, socleC2×C3×C52×C109C2
LCSG ▷ C3×C5×C109
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6540

Conjugacy classes & character table

8190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32700, 214);