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C11×C25×C22⋊ΓL(1,𝔽8) #37528312

order23100
automorphism?
homologyAbelianization (H1) = C3×C11×C25 · Schur multiplier (H2) = C2

Aliases

direct productC11×C25×C22⋊ΓL(1,𝔽8)
unambiguous semidirect productC22⋊(C11×ΓL(1,𝔽8)×C25)
unambiguous semidirect productC7⋊(C11×A4×C25)
unambiguous semidirect product(C22×C25)⋊(C11×ΓL(1,𝔽8))
unambiguous semidirect product(C7×C25)⋊(C11×A4)
unambiguous semidirect product(C22×C11×C25)⋊ΓL(1,𝔽8)
unambiguous semidirect product(C7×C11×C25)⋊A4

Splittings

Fitting, HallC22×C7×C11×C25 ⋊ C3
derived, HallC22×C7 ⋊ C3×C11×C25
HallC7×C11×C25 ⋊ A4
HallC22×C11×C25 ⋊ ΓL(1,𝔽8)
HallC22×C7×C25 ⋊ C3×C11
HallC22×C7×C11 ⋊ C3×C25
HallC7×C25 ⋊ C11×A4
HallC22×C25 ⋊ C11×ΓL(1,𝔽8)
HallC7×C11 ⋊ A4×C25
HallC22×C11 ⋊ ΓL(1,𝔽8)×C25
SylowC7 ⋊ C11×A4×C25
SylowC22 ⋊ C11×ΓL(1,𝔽8)×C25

Subgroups

subgroupG/H
center, hypercenterC11×C25C22⋊ΓL(1,𝔽8)
commutator, hypocenterC22×C7C3×C11×C25
FrattiniC5C5×C11×C22⋊ΓL(1,𝔽8)
FittingC22×C7×C11×C25C3
socleC22×C5×C7×C11C3×C5
prime radicalC5×C11×C22⋊ΓL(1,𝔽8)C5
cosocleC22×C5×C7C3×C5×C11
LCSG ▷ C22×C7
UCSC1 ◁ C11×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7700

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 123);