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C3×Dic13×ΓL(1,𝔽32) #37563728

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

Aliases

direct productC3×Dic13×ΓL(1,𝔽32)
unambiguous semidirect product(C3×C31×Dic13)⋊C5

Splittings

derived, HallC13×C31 ⋊ C3×C4×C5
HallC3×C13×ΓL(1,𝔽32) ⋊ C4
HallC3×C31×Dic13 ⋊ C5
HallC13×ΓL(1,𝔽32) ⋊ C3×C4
HallC31×Dic13 ⋊ C3×C5
HallC3×C13×C31 ⋊ C4×C5
HallC3×C31 ⋊ C5×Dic13
HallC3×C13 ⋊ C4×ΓL(1,𝔽32)
SylowC31 ⋊ C3×C5×Dic13
SylowC13 ⋊ C3×C4×ΓL(1,𝔽32)

Subgroups

subgroupG/H
center, hypercenterC2×C3D13×ΓL(1,𝔽32)
commutator, hypocenterC13×C31C3×C4×C5
FrattiniC2C3×D13×ΓL(1,𝔽32)
Fitting, socleC2×C3×C13×C31C2×C5
prime radicalC2×C3×C13×ΓL(1,𝔽32)C2
cosocleC2×C13×C31C2×C3×C5
LCSG ▷ C13×C31
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4836

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 27);