Finite Group Databasebeta

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C2×C5×D11×#4296 #49178564

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

Aliases

direct productC2×C5×D11×#4296

Splittings

Fitting, socleC2×C5×C11×C19 ⋊ C2×C9
derived, HallC11×C19 ⋊ C22×C5×C9
HallC5×C11×#4296 ⋊ C22
HallC2×C5×C19×D11 ⋊ C9
HallC11×#4296 ⋊ C22×C5
HallC5×C11×C19 ⋊ C22×C9
HallC2×C19×D11 ⋊ C5×C9
HallC5×C19 ⋊ C2×C9×D11
HallC5×C11 ⋊ C22×#4296
SylowC19 ⋊ C2×C5×C9×D11
SylowC11 ⋊ C22×C5×#4296

Subgroups

subgroupG/H
center, hypercenterC2×C5D11×#4296
commutator, hypocenterC11×C19C22×C5×C9
FrattiniC1G
Fitting, socleC2×C5×C11×C19C2×C9
prime radicalC2×C5×D11×C19⋊C3C3
cosocleC11×C19⋊C3C22×C3×C5
LCSG ▷ C11×C19
UCSC1 ◁ C2×C5

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2090

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 273);