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C4×C13×(C31⋊C3)⋊C5 #37563708

order24180
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC4×C13×(C31⋊C3)⋊C5
unambiguous semidirect product(C4×C31⋊C3)⋊(C5×C13)
unambiguous semidirect product(C4×ΓL(1,𝔽32))⋊(C3×C13)
unambiguous semidirect product(C4×C13×C31⋊C3)⋊C5

Splittings

Fitting, HallC4×C13×C31 ⋊ C3×C5
derived, SylowC31 ⋊ C3×C4×C5×C13
HallC4×C13×ΓL(1,𝔽32) ⋊ C3
HallC4×C13×C31⋊C3 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C3×C4
HallC13×C31⋊C3 ⋊ C4×C5
HallC4×ΓL(1,𝔽32) ⋊ C3×C13
HallC13×C31 ⋊ C3×C4×C5
HallC4×C31⋊C3 ⋊ C5×C13
HallΓL(1,𝔽32) ⋊ C3×C4×C13
HallC4×C31 ⋊ C3×C5×C13
HallC31⋊C3 ⋊ C4×C5×C13

Subgroups

subgroupG/H
center, hypercenterC4×C13(C31⋊C3)⋊C5
commutator, hypocenterC31C3×C4×C5×C13
FrattiniC2C2×C13×(C31⋊C3)⋊C5
FittingC4×C13×C31C3×C5
socleC2×C13×C31C2×C3×C5
prime radicalC2×C13×(C31⋊C3)⋊C5C2
cosocleC2×C31C2×C3×C5×C13
LCSG ▷ C31
UCSC1 ◁ C4×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1612

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 7);