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C2×C5×ΓL(1,𝔽8)⋊D73 #44501369

order30660
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×ΓL(1,𝔽8)⋊D73
unambiguous semidirect product(C2×ΓL(1,𝔽8))⋊(C5×D73)

Splittings

Fitting, socleC2×C5×C7×C73 ⋊ C2×C3
derived, HallC7×C73 ⋊ C22×C3×C5
HallC2×C5×D511 ⋊ C3
HallC5×ΓL(1,𝔽8)×C73 ⋊ C22
HallC5×C7×C73 ⋊ C22×C3
HallC2×D511 ⋊ C3×C5
HallΓL(1,𝔽8)×C73 ⋊ C22×C5
HallC5×C73 ⋊ C2×AGL(1,𝔽7)
HallC5×ΓL(1,𝔽8) ⋊ C2×D73
SylowC73 ⋊ C2×C5×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×C3×D73
HallΓL(1,𝔽8) ⋊ C2×C5×D73
SylowC7 ⋊ C2×C3×C5×D73

Subgroups

subgroupG/H
center, hypercenterC2×C5ΓL(1,𝔽8)⋊D73
commutator, cosocle, hypocenterC7×C73C22×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C73C2×C3
LCSG ▷ C7×C73
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5110

Conjugacy classes & character table

1870 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 132);