Finite Group Databasebeta

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C2×C5×D11×#4294 #49178363

order37620
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D11×#4294

Splittings

derived, HallC11×C19 ⋊ C22×C5×C9
HallC5×C11×#4294 ⋊ C22
HallC2×C5×C19×D11 ⋊ C9
HallC11×#4294 ⋊ C22×C5
HallC5×C11×C19 ⋊ C22×C9
HallC2×C19×D11 ⋊ C5×C9
HallC5×C19 ⋊ C2×C9×D11
HallC5×C11 ⋊ C22×#4294
SylowC19 ⋊ C2×C5×C9×D11
SylowC11 ⋊ C22×C5×#4294

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D11×C19⋊C3
commutator, hypocenterC11×C19C22×C5×C9
FrattiniC3C2×C5×D11×C19⋊C3
Fitting, socleC2×C3×C5×C11×C19C2×C3
prime radicalC2×C3×C5×C19×D11C3
cosocleC3×C11×C19C22×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C2×C3×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18810

Conjugacy classes & character table

1890 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 72);