Finite Group Databasebeta

← Prev (#30655300) Next (#30655302) →

ΓL(1,𝔽8)×#63118⋊C3 #30655301

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

Aliases

direct productΓL(1,𝔽8)×#63118⋊C3
unambiguous semidirect product(C7×#63118⋊C3)⋊C3
unambiguous semidirect product#19129772⋊C3
unambiguous semidirect product#19129773⋊C3
unambiguous semidirect product(ΓL(1,𝔽8)×#63118)⋊C3

Splittings

Fitting, socle, derived, HallC5×C7×C13 ⋊ C32×C4
HallC5×ΓL(1,𝔽8)×C13⋊C3 ⋊ C4
HallC7×#63118 ⋊ C32
HallΓL(1,𝔽8)×C13⋊C3 ⋊ Dic5
Hall#63118 ⋊ C3×ΓL(1,𝔽8)
HallC7×C13 ⋊ C32×Dic5
HallC5×C13 ⋊ C3×C4×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×AGL(1,𝔽13)
SylowC13 ⋊ C3×Dic5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×#63118⋊C3
SylowC5 ⋊ ΓL(1,𝔽8)×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C13C32×C4
prime radicalC5×ΓL(1,𝔽8)×D13⋊C3C2
cosocleC5×C7×D13C2×C32
LCSG ▷ C5×C7×C13
UCSC1

144 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 455

Conjugacy classes & character table

145 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 351);