Finite Group Databasebeta

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C2×D5×#13131976 #46776529

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

Aliases

direct productC2×D5×#13131976
unambiguous semidirect productC5⋊(C22×#13131976)
unambiguous semidirect product(C2×C5)⋊(C2×#13131976)

Splittings

Fitting, socleC2×C5×C13×C43 ⋊ C2×C3
derived, HallC5×C13×C43 ⋊ C22×C3
HallC2×D5×C13×C43 ⋊ C3
HallC5×#13131976 ⋊ C22
HallC2×D5×C43 ⋊ C13⋊C3
HallC13×C43 ⋊ C2×C3×D5
HallC2×D5×C13 ⋊ C43⋊C3
HallC5×C43 ⋊ C22×C13⋊C3
HallC5×C13 ⋊ C22×C43⋊C3
SylowC43 ⋊ C2×D5×C13⋊C3
SylowC13 ⋊ C2×D5×C43⋊C3
SylowC5 ⋊ C22×#13131976

Subgroups

subgroupG/H
center, hypercenterC2D5×#13131976
commutator, cosocle, hypocenterC5×C13×C43C22×C3
FrattiniC1G
Fitting, socleC2×C5×C13×C43C2×C3
LCSG ▷ C5×C13×C43
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5590

Conjugacy classes & character table

1512 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 149);