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C3×C5×ΓL(1,𝔽8)⋊#261 #30655315

order16380
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×ΓL(1,𝔽8)⋊#261
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×C5×#261)

Splittings

Fitting, socleC3×C5×C7×C13 ⋊ C3×C4
derived, HallC7×C13 ⋊ C32×C4×C5
HallC3×C5×C13×ΓL(1,𝔽8) ⋊ C4
HallC5×C7⋊#261 ⋊ C32
HallC3×C13×ΓL(1,𝔽8) ⋊ C4×C5
HallC5×C7×C13 ⋊ C32×C4
HallC7⋊#261 ⋊ C32×C5
HallC3×C5×ΓL(1,𝔽8) ⋊ #261
HallC5×C13 ⋊ C3×ΓL(1,𝔽8)⋊C4
HallC3×ΓL(1,𝔽8) ⋊ C5×#261
HallC5×C7 ⋊ C32×#261
SylowC13 ⋊ C3×C5×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C32×C5×#261

Subgroups

subgroupG/H
center, hypercenterC3×C5ΓL(1,𝔽8)⋊#261
commutator, hypocenterC7×C13C32×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×C5×ΓL(1,𝔽8)×D13C2
cosocleC7×D13C2×C32×C5
LCSG ▷ C7×C13
UCSC1 ◁ C3×C5

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1365

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 365);