Finite Group Databasebeta

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C2×C5⋊#16809814 #46776524

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

Aliases

direct productC2×C5⋊#16809814
unambiguous semidirect product(C2×C5)⋊#16809814

Splittings

Fitting, socleC2×C5×C13×C43 ⋊ C2×C3
derived, HallC5×C13×C43 ⋊ C22×C3
HallC2×C43×D65 ⋊ C3
HallC5×#13131975 ⋊ C22
Hall#13131975 ⋊ C2×D5
HallC13×C43 ⋊ C2×C3×D5
HallC2×D65 ⋊ C43⋊C3
HallC5×C43 ⋊ C2×D13⋊C3
HallC5×C13 ⋊ C22×C43⋊C3
SylowC43 ⋊ C2×C5⋊(D13⋊C3)
SylowC13 ⋊ C2×D5×C43⋊C3
SylowC5 ⋊ C2×#16809814

Subgroups

subgroupG/H
center, hypercenterC2C5⋊#16809814
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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 144);