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C2×C13⋊C3×D31⋊C5 #37563796

order24180
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13⋊C3×D31⋊C5
unambiguous semidirect product(C2×C13⋊C3×D31)⋊C5

Splittings

Fitting, socleC2×C13×C31 ⋊ C2×C3×C5
derived, HallC13×C31 ⋊ C22×C3×C5
HallC2×C13×D31⋊C5 ⋊ C3
HallC13⋊C3×ΓL(1,𝔽32) ⋊ C22
HallC2×C13⋊C3×D31 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C22×C3
HallC2×C13×D31 ⋊ C3×C5
HallC31×C13⋊C3 ⋊ C22×C5
HallΓL(1,𝔽32) ⋊ C22×C13⋊C3
HallC2×D31 ⋊ C5×C13⋊C3
SylowC31 ⋊ C22×C5×C13⋊C3
SylowC13 ⋊ C2×C3×D31⋊C5

Subgroups

subgroupG/H
center, hypercenterC2C13⋊C3×D31⋊C5
commutator, cosocle, hypocenterC13×C31C22×C3×C5
FrattiniC1G
Fitting, socleC2×C13×C31C2×C3×C5
LCSG ▷ C13×C31
UCSC1 ◁ C2

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 806

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 95);