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C5×ΓL(1,𝔽8)×Dic13⋊C3 #30655190

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

Aliases

direct productC5×ΓL(1,𝔽8)×Dic13⋊C3
unambiguous semidirect product(C7×Dic13⋊C3)⋊(C3×C5)
unambiguous semidirect product(ΓL(1,𝔽8)×Dic13)⋊(C3×C5)
unambiguous semidirect product#11763957⋊(C3×C5)
unambiguous semidirect product#11763958⋊(C3×C5)
unambiguous semidirect product(C5×C7×Dic13⋊C3)⋊C3
unambiguous semidirect product(C5×ΓL(1,𝔽8)×Dic13)⋊C3
unambiguous semidirect product(C5×#11763957)⋊C3
unambiguous semidirect product(C5×#11763958)⋊C3

Splittings

derived, HallC7×C13 ⋊ C32×C4×C5
HallC5×ΓL(1,𝔽8)×C13⋊C3 ⋊ C4
HallC5×C7×Dic13 ⋊ C32
HallΓL(1,𝔽8)×C13⋊C3 ⋊ C4×C5
HallC5×C7×C13 ⋊ C32×C4
HallC7×Dic13 ⋊ C32×C5
HallC5×Dic13 ⋊ C3×ΓL(1,𝔽8)
HallC5×C13 ⋊ C3×C4×ΓL(1,𝔽8)
HallDic13 ⋊ C3×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×Dic13⋊C3
SylowC13 ⋊ C3×C4×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C5×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)×D13⋊C3
commutator, hypocenterC7×C13C32×C4×C5
FrattiniC2C5×ΓL(1,𝔽8)×D13⋊C3
Fitting, socleC2×C5×C7×C13C2×C32
prime radicalC2×C5×ΓL(1,𝔽8)×C13⋊C3C2
cosocleC2×C7×C13C2×C32×C5
LCSG ▷ C7×C13
UCSC1 ◁ C2×C5

144 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 1820

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 240);