Finite Group Databasebeta

← Prev (#49178366) Next (#49178368) →

C2×D55×#4294 #49178367

order37620
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×D55×#4294
unambiguous semidirect product(C2×C5)⋊(D11×#4294)
unambiguous semidirect product(C2×C11)⋊(D5×#4294)

Splittings

derived, HallC5×C11×C19 ⋊ C22×C9
HallC5×C11×#4294 ⋊ C22
HallC2×C19×D55 ⋊ C9
HallC11×#4294 ⋊ C2×D5
HallC5×#4294 ⋊ C2×D11
HallC11×C19 ⋊ C2×C9×D5
HallC5×C19 ⋊ C2×C9×D11
HallC5×C11 ⋊ C22×#4294
SylowC19 ⋊ C2×C9×D55
SylowC11 ⋊ C2×D5×#4294
SylowC5 ⋊ C2×D11×#4294

Subgroups

subgroupG/H
center, hypercenterC2×C3C19⋊C3×D55
commutator, hypocenterC5×C11×C19C22×C9
FrattiniC3C2×C19⋊C3×D55
Fitting, socleC2×C3×C5×C11×C19C2×C3
prime radicalC2×C3×C19×D55C3
cosocleC3×C5×C11×C19C22×C3
LCSG ▷ C5×C11×C19
UCSC1 ◁ C2×C3

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18810

Conjugacy classes & character table

1566 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 76);