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C2×C5×ΓL(1,𝔽8)⋊D79 #45684469

order33180
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×ΓL(1,𝔽8)⋊D79
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C5×D79)

Splittings

Fitting, socleC2×C5×C7×C79 ⋊ C2×C3
derived, HallC7×C79 ⋊ C22×C3×C5
HallC2×C5×D553 ⋊ C3
HallC5×ΓL(1,𝔽8)×C79 ⋊ C22
HallC5×C7×C79 ⋊ C22×C3
HallC2×D553 ⋊ C3×C5
HallΓL(1,𝔽8)×C79 ⋊ C22×C5
HallC5×C79 ⋊ C2×AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ C2×D79
SylowC79 ⋊ C2×C5×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×C3×D79
HallΓL(1,𝔽8) ⋊ C2×C5×D79
SylowC7 ⋊ C2×C3×C5×D79

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)⋊D79
commutator, cosocle, hypocenterC7×C79C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C79C2×C3
LCSG ▷ C7×C79
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5530

Conjugacy classes & character table

2020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33180, 100);