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C3×ΓL(1,𝔽8)×Dic65 #30655221

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

Aliases

direct productC3×ΓL(1,𝔽8)×Dic65

Splittings

derived, HallC5×C7×C13 ⋊ C32×C4
HallC3×C5×C13×ΓL(1,𝔽8) ⋊ C4
HallC7×Dic65 ⋊ C32
HallC3×C13×ΓL(1,𝔽8) ⋊ Dic5
HallC3×C5×ΓL(1,𝔽8) ⋊ Dic13
HallC7×C13 ⋊ C32×Dic5
HallC5×C13 ⋊ C3×C4×ΓL(1,𝔽8)
HallC5×C7 ⋊ C32×Dic13
SylowC13 ⋊ C3×Dic5×ΓL(1,𝔽8)
SylowC7 ⋊ C32×Dic65
SylowC5 ⋊ C3×ΓL(1,𝔽8)×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C3ΓL(1,𝔽8)×D65
commutator, hypocenterC5×C7×C13C32×C4
FrattiniC2C3×ΓL(1,𝔽8)×D65
Fitting, socleC2×C3×C5×C7×C13C2×C3
prime radicalC2×C3×C5×C13×ΓL(1,𝔽8)C2
cosocleC2×C5×C7×C13C2×C32
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2×C3

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5460

Conjugacy classes & character table

1020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 271);