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C2×ΓL(1,𝔽8)×D275 #37528265

order23100
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×ΓL(1,𝔽8)×D275
unambiguous semidirect product(C2×C11)⋊(ΓL(1,𝔽8)×D25)
unambiguous semidirect product(C2×C25)⋊(ΓL(1,𝔽8)×D11)
unambiguous semidirect product(C2×C7×D275)⋊C3

Splittings

FittingC2×C7×C11×C25 ⋊ C2×C3
derived, HallC7×C11×C25 ⋊ C22×C3
HallC2×C7×D275 ⋊ C3
HallC11×ΓL(1,𝔽8)×C25 ⋊ C22
HallΓL(1,𝔽8)×C25 ⋊ C2×D11
HallC11×C25 ⋊ C22×ΓL(1,𝔽8)
HallC11×ΓL(1,𝔽8) ⋊ C2×D25
HallC7×C25 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D25
SylowC25 ⋊ C2×ΓL(1,𝔽8)×D11
SylowC11 ⋊ C2×ΓL(1,𝔽8)×D25
SylowC7 ⋊ C2×C3×D275

Subgroups

subgroupG/H
center, hypercenterC2ΓL(1,𝔽8)×D275
commutator, cosocle, hypocenterC7×C11×C25C22×C3
FrattiniC5C2×ΓL(1,𝔽8)×D55
FittingC2×C7×C11×C25C2×C3
socleC2×C5×C7×C11C3×D5
LCSG ▷ C7×C11×C25
UCSC1 ◁ C2

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3850

Conjugacy classes & character table

1390 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 76);