Finite Group Databasebeta

← Prev (#19154147) Next (#19154149) →

C2×C5⋊(D97⋊C3) #19154148

order5820
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊(D97⋊C3)
unambiguous semidirect product(C2×C5)⋊(D97⋊C3)
unambiguous semidirect product(C2×C97⋊C3)⋊D5
unambiguous semidirect product(C2×D485)⋊C3

Splittings

Fitting, socleC2×C5×C97 ⋊ C2×C3
derived, HallC5×C97 ⋊ C22×C3
HallC2×D485 ⋊ C3
HallC5×C97⋊C3 ⋊ C22
HallC97⋊C3 ⋊ C2×D5
SylowC97 ⋊ C2×C3×D5
SylowC5 ⋊ C2×D97⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C5⋊(D97⋊C3)
commutator, hypocenterC5×C97C22×C3
FrattiniC1G
Fitting, socleC2×C5×C97C2×C3
LCSG ▷ C5×C97
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

184 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×C5⋊(D97⋊C3), C2×C3×C5⋊(D97⋊C3), C2×C3⋊(C5⋊(D97⋊C3)), …
maximal normal subgroup ofC2×C3×C5⋊(D97⋊C3), C2×C5×C5⋊(D97⋊C3)
maximal quotient ofC2×C5⋊(D97⋊C9), D3×C5⋊(D97⋊C3), C2×C3×C5⋊(D97⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5820, 22);