Finite Group Databasebeta

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C2×C52×D109⋊C3 #45658299

order32700
automorphism?
homologyAbelianization (H1) = C22×C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C52×D109⋊C3
unambiguous semidirect productD109⋊(C2×C3×C52)
unambiguous semidirect product(C109⋊C3)⋊(C22×C52)
unambiguous semidirect product(C2×D109)⋊(C3×C52)
unambiguous semidirect product(C2×C109⋊C3)⋊(C2×C52)
unambiguous semidirect product(C2×C5×D109)⋊(C3×C5)

Splittings

Fitting, socleC2×C52×C109 ⋊ C2×C3
derived, SylowC109 ⋊ C22×C3×C52
HallC2×C52×D109 ⋊ C3
HallC52×C109⋊C3 ⋊ C22
HallC52×C109 ⋊ C22×C3
HallC2×D109 ⋊ C3×C52
HallC109⋊C3 ⋊ C22×C52

Subgroups

subgroupG/H
center, hypercenterC2×C52D109⋊C3
commutator, cosocle, hypocenterC109C22×C3×C52
FrattiniC1G
Fitting, socleC2×C52×C109C2×C3
LCSG ▷ C109
UCSC1 ◁ C2×C52

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5450

Conjugacy classes & character table

1200 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32700, 135);