Finite Group Databasebeta

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C2×C5⋊#16809809 #46776527

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

Aliases

direct productC2×C5⋊#16809809
unambiguous semidirect product(C2×C5)⋊#16809809

Splittings

Fitting, socleC2×C5×C13×C43 ⋊ C2×C3
derived, HallC5×C13×C43 ⋊ C22×C3
HallC2×C13×D215 ⋊ C3
HallC5×#13131976 ⋊ C22
Hall#13131976 ⋊ C2×D5
HallC2×D215 ⋊ C13⋊C3
HallC13×C43 ⋊ C2×C3×D5
HallC5×C43 ⋊ C22×C13⋊C3
HallC5×C13 ⋊ C2×D43⋊C3
SylowC43 ⋊ C2×D5×C13⋊C3
SylowC13 ⋊ C2×C5⋊(D43⋊C3)
SylowC5 ⋊ C2×#16809809

Subgroups

subgroupG/H
center, hypercenterC2C5⋊#16809809
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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33540, 147);