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C3×ΓL(1,𝔽32)⋊#261 #37563799

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

Aliases

direct productC3×ΓL(1,𝔽32)⋊#261
unambiguous semidirect product(C3×C31⋊#261)⋊C5

Splittings

Fitting, socle, HallC3×C13×C31 ⋊ C4×C5
derived, HallC13×C31 ⋊ C3×C4×C5
HallC3×C13×ΓL(1,𝔽32) ⋊ C4
HallC3×C31⋊#261 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C3×C4
HallC31⋊#261 ⋊ C3×C5
HallC3×ΓL(1,𝔽32) ⋊ #261
HallΓL(1,𝔽32) ⋊ C3×#261
HallC3×C31 ⋊ C5×#261
HallC3×C13 ⋊ Dic31⋊C5
SylowC31 ⋊ C3×C5×#261
SylowC13 ⋊ C3×Dic31⋊C5

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽32)⋊#261
commutator, hypocenterC13×C31C3×C4×C5
FrattiniC1G
Fitting, socleC3×C13×C31C4×C5
prime radicalC3×D13×ΓL(1,𝔽32)C2
cosocleD13×C31C2×C3×C5
LCSG ▷ C13×C31
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1209

Conjugacy classes & character table

177 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 98);