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C2×C5×C3⋊(D109⋊C3) #34087145

order19620
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C3⋊(D109⋊C3)
unambiguous semidirect product(C2×C3)⋊(C5×D109⋊C3)
unambiguous semidirect product(C2×C109⋊C3)⋊(C5×D3)
unambiguous semidirect product(C2×D327)⋊(C3×C5)
unambiguous semidirect product(C2×C5×D327)⋊C3

Splittings

Fitting, socleC2×C3×C5×C109 ⋊ C2×C3
derivedC3×C109 ⋊ C22×C3×C5
HallC3×C5×C109⋊C3 ⋊ C22
HallC3×C109⋊C3 ⋊ C22×C5
HallC5×C109 ⋊ C2×C3×D3
SylowC109 ⋊ C2×C3×C5×D3

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊(D109⋊C3)
commutator, cosocle, hypocenterC3×C109C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C109C2×C3
LCSG ▷ C3×C109
UCSC1 ◁ C2×C5

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3270

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19620, 113);