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C2×((C31⋊C3)⋊C5)⋊D13 #37563797

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

Aliases

direct productC2×((C31⋊C3)⋊C5)⋊D13
unambiguous semidirect product(C2×(C31⋊C3)⋊C5)⋊D13
unambiguous semidirect product(C2×(C31⋊C3)⋊D13)⋊C5

Splittings

Fitting, socleC2×C13×C31 ⋊ C2×C3×C5
derived, HallC13×C31 ⋊ C22×C3×C5
HallC2×C13⋊(D31⋊C5) ⋊ C3
HallC13×(C31⋊C3)⋊C5 ⋊ C22
HallC2×(C31⋊C3)⋊D13 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C22×C3
HallC2×D403 ⋊ C3×C5
HallC13×C31⋊C3 ⋊ C22×C5
Hall(C31⋊C3)⋊C5 ⋊ C2×D13
HallΓL(1,𝔽32) ⋊ C2×C3×D13
HallC31⋊C3 ⋊ C2×C5×D13
SylowC31 ⋊ C2×C3×C5×D13
SylowC13 ⋊ C2×AGL(1,𝔽31)

Subgroups

subgroupG/H
center, hypercenterC2((C31⋊C3)⋊C5)⋊D13
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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 96);