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#261×(C31⋊C3)⋊C5 #37563785

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

Aliases

direct product#261×(C31⋊C3)⋊C5
unambiguous semidirect product(#261×C31⋊C3)⋊C5

Splittings

Fitting, socle, derived, HallC13×C31 ⋊ C3×C4×C5
Hall#261×ΓL(1,𝔽32) ⋊ C3
HallC13×(C31⋊C3)⋊C5 ⋊ C4
Hall#261×C31⋊C3 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C3×C4
HallC31×#261 ⋊ C3×C5
HallC13×C31⋊C3 ⋊ C4×C5
HallΓL(1,𝔽32) ⋊ C3×#261
HallC31⋊C3 ⋊ C5×#261
SylowC31 ⋊ C3×C5×#261
SylowC13 ⋊ C4×(C31⋊C3)⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC13×C31C3×C4×C5
prime radicalD13×(C31⋊C3)⋊C5C2
cosocleD13×C31C2×C3×C5
LCSG ▷ C13×C31
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 403

Conjugacy classes & character table

119 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 84);