Finite Group Databasebeta

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C2×C5×#16809809 #46776513

order33540
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×#16809809

Splittings

Fitting, socleC2×C5×C13×C43 ⋊ C2×C3
derived, HallC13×C43 ⋊ C22×C3×C5
HallC2×C5×C13×D43 ⋊ C3
HallC5×#13131976 ⋊ C22
HallC5×C13×C43 ⋊ C22×C3
HallC2×C13×D43 ⋊ C3×C5
Hall#13131976 ⋊ C22×C5
HallC2×C5×D43 ⋊ C13⋊C3
HallC5×C43 ⋊ C22×C13⋊C3
HallC2×D43 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ C2×D43⋊C3
SylowC43 ⋊ C22×C5×C13⋊C3
SylowC13 ⋊ C2×C5×D43⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#16809809
commutator, cosocle, hypocenterC13×C43C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C13×C43C2×C3
LCSG ▷ C13×C43
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5590

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 133);