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C2×D5×ΓL(1,𝔽8)×C73 #44501383

order30660
automorphism?
homologyAbelianization (H1) = C22×C3×C73 · Schur multiplier (H2) = C2

Aliases

direct productC2×D5×ΓL(1,𝔽8)×C73
unambiguous semidirect productC5⋊(C22×ΓL(1,𝔽8)×C73)
unambiguous semidirect product(C2×C5)⋊(C2×ΓL(1,𝔽8)×C73)
unambiguous semidirect product(C2×C7×D5)⋊(C3×C73)

Splittings

Fitting, socleC2×C5×C7×C73 ⋊ C2×C3
derived, HallC5×C7 ⋊ C22×C3×C73
HallC2×C7×D5×C73 ⋊ C3
HallC5×ΓL(1,𝔽8)×C73 ⋊ C22
HallC5×C7×C73 ⋊ C22×C3
HallC7×C73 ⋊ C2×C3×D5
HallC5×C73 ⋊ C22×ΓL(1,𝔽8)
HallC2×C7×D5 ⋊ C3×C73
HallC5×ΓL(1,𝔽8) ⋊ C22×C73
SylowC7 ⋊ C2×C3×D5×C73
SylowC5 ⋊ C22×ΓL(1,𝔽8)×C73

Subgroups

subgroupG/H
center, hypercenterC2×C73D5×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC5×C7C22×C3×C73
FrattiniC1G
Fitting, socleC2×C5×C7×C73C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C2×C73

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5110

Conjugacy classes & character table

2920 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30660, 146);