Finite Group Databasebeta

← Prev (#21440952) Next (#21440954) →

C2×C5×C3⋊D129 #21440953

order7740
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C5×C3⋊D129
unambiguous semidirect product(C2×C3)⋊(C5×D129)
unambiguous semidirect product(C2×C43)⋊(C5×C3⋊D3)

Splittings

Fitting, socleC2×C32×C5×C43 ⋊ C2
derived, HallC32×C43 ⋊ C22×C5
HallC32×C5×C43 ⋊ C22
HallC5×C43 ⋊ C2×C3⋊D3
HallC32×C5 ⋊ C2×D43
SylowC43 ⋊ C2×C5×C3⋊D3
SylowC32 ⋊ C2×C5×D43

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊D129
commutator, hypocenterC32×C43C22×C5
FrattiniC1G
Fitting, socleC2×C32×C5×C43C2
LCSG ▷ C32×C43
UCSC1 ◁ C2×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1950 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7740, 121);