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C11×ΓL(1,𝔽8)×#1035 #37528244

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)×#1035
unambiguous semidirect product(C7×#1035)⋊(C3×C11)
unambiguous semidirect product(C7×C11×#1035)⋊C3

Splittings

Fitting, HallC7×C11×C25 ⋊ C3×C4
derived, HallC7×C25 ⋊ C3×C4×C11
HallC7×C11×#1035 ⋊ C3
HallC11×ΓL(1,𝔽8)×C25 ⋊ C4
HallC7×#1035 ⋊ C3×C11
HallΓL(1,𝔽8)×C25 ⋊ C4×C11
HallC11×C25 ⋊ C4×ΓL(1,𝔽8)
HallC7×C11 ⋊ C3×#1035
SylowC25 ⋊ C4×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C11×#1035

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)×#1035
commutator, hypocenterC7×C25C3×C4×C11
FrattiniC5C11×AGL(1,𝔽5)×ΓL(1,𝔽8)
FittingC7×C11×C25C3×C4
socleC5×C7×C11C3×AGL(1,𝔽5)
prime radicalC11×ΓL(1,𝔽8)×D25C2
cosocleC7×D25C2×C3×C11
LCSG ▷ C7×C25
UCSC1 ◁ C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1925

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 55);