Finite Group Databasebeta

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C2×C32×C5×D209 #49178773

order37620
automorphism?
homologyAbelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×C5×D209

Splittings

Fitting, socleC2×C32×C5×C11×C19 ⋊ C2
derived, HallC11×C19 ⋊ C22×C32×C5
HallC32×C5×C11×C19 ⋊ C22
HallC32×C11×C19 ⋊ C22×C5
HallC5×C11×C19 ⋊ C22×C32
HallC32×C5×C19 ⋊ C2×D11
HallC32×C5×C11 ⋊ C2×D19
HallC32×C19 ⋊ C2×C5×D11
HallC32×C11 ⋊ C2×C5×D19
HallC5×C19 ⋊ C2×C32×D11
HallC5×C11 ⋊ C2×C32×D19
SylowC19 ⋊ C2×C32×C5×D11
SylowC11 ⋊ C2×C32×C5×D19

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5D209
commutator, cosocle, hypocenterC11×C19C22×C32×C5
FrattiniC1G
Fitting, socleC2×C32×C5×C11×C19C2
LCSG ▷ C11×C19
UCSC1 ◁ C2×C32×C5

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18810

Conjugacy classes & character table

9540 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 482);