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C2×C5×#13131975 #30680781

order16770
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×#13131975

Splittings

Fitting, socle, HallC2×C5×C13×C43 ⋊ C3
derived, HallC13×C43 ⋊ C2×C3×C5
HallC5×C13×C43 ⋊ C2×C3
HallC2×C13×C43 ⋊ C3×C5
HallC2×C5×C43 ⋊ C13⋊C3
HallC5×C43 ⋊ C2×C13⋊C3
HallC2×C5×C13 ⋊ C43⋊C3
HallC2×C43 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ C2×C43⋊C3
SylowC43 ⋊ C2×C5×C13⋊C3
HallC2×C13 ⋊ C5×C43⋊C3
SylowC13 ⋊ C2×C5×C43⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#13131975
commutator, cosocle, hypocenterC13×C43C2×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C13×C43C3
LCSG ▷ C13×C43
UCSC1 ◁ C2×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5590

Conjugacy classes & character table

1890 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×#13131975, C5×#20269436, C5×#20269440, …
maximal normal subgroup ofC4×C5×#13131975, C5×#20269436, C5×#20269440, …
maximal quotient ofC4×C5×#13131975, C22×C5×#13131975

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16770, 5);