Finite Group Databasebeta

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C2×C5⋊(D103⋊C9) #32915170

order18540
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊(D103⋊C9)
unambiguous semidirect product(C2×C5)⋊(D103⋊C9)
unambiguous semidirect product(C2×C103⋊C9)⋊D5
unambiguous semidirect product(C2×D515)⋊C9

Splittings

derived, HallC5×C103 ⋊ C22×C9
HallC5×C103⋊C9 ⋊ C22
HallC2×D515 ⋊ C9
HallC103⋊C9 ⋊ C2×D5
SylowC103 ⋊ C2×C9×D5
SylowC5 ⋊ C2×D103⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊(D103⋊C3)
commutator, hypocenterC5×C103C22×C9
FrattiniC3C2×C5⋊(D103⋊C3)
Fitting, socleC2×C3×C5×C103C2×C3
prime radicalC2×C3×D515C3
cosocleC3×C5×C103C22×C3
LCSG ▷ C5×C103
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9270

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18540, 18);