Finite Group Databasebeta

← Prev (#30655336) Next (#30655338) →

C3×ΓL(1,𝔽8)⋊#63120 #30655337

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

Aliases

direct productC3×ΓL(1,𝔽8)⋊#63120
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×#63120)

Splittings

Fitting, socleC3×C5×C7×C13 ⋊ C3×C4
derived, HallC5×C7×C13 ⋊ C32×C4
HallC3×C5×C13×ΓL(1,𝔽8) ⋊ C4
HallC7⋊#63120 ⋊ C32
HallC3×C13×ΓL(1,𝔽8) ⋊ AGL(1,𝔽5)
HallC3×C5×ΓL(1,𝔽8) ⋊ Dic13
HallC7×C13 ⋊ C32×AGL(1,𝔽5)
HallC5×C13 ⋊ C3×ΓL(1,𝔽8)⋊C4
HallC3×ΓL(1,𝔽8) ⋊ #63120
HallC5×C7 ⋊ C32×Dic13
SylowC13 ⋊ C3×ΓL(1,𝔽8)⋊AGL(1,𝔽5)
SylowC7 ⋊ C32×#63120
SylowC5 ⋊ C3×ΓL(1,𝔽8)⋊Dic13

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)⋊#63120
commutator, hypocenterC5×C7×C13C32×C4
FrattiniC1G
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×D5×C13×ΓL(1,𝔽8)C2
cosocleC7×D5×C13C2×C32
LCSG ▷ C5×C7×C13
UCSC1 ◁ C3

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1365

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 387);