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ΓL(1,𝔽8)×C11⋊#1035 #37528245

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

Aliases

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

Splittings

Fitting, derived, HallC7×C11×C25 ⋊ C3×C4
HallC7×C11⋊#1035 ⋊ C3
HallC11×ΓL(1,𝔽8)×C25 ⋊ C4
HallΓL(1,𝔽8)×C25 ⋊ Dic11
HallC11×C25 ⋊ C4×ΓL(1,𝔽8)
HallC11×ΓL(1,𝔽8) ⋊ #1035
HallC7×C25 ⋊ C3×Dic11
HallC7×C11 ⋊ C3×#1035
SylowC25 ⋊ ΓL(1,𝔽8)×Dic11
SylowC11 ⋊ ΓL(1,𝔽8)×#1035
SylowC7 ⋊ C3×C11⋊#1035

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, hypocenterC7×C11×C25C3×C4
FrattiniC5ΓL(1,𝔽8)×C11⋊AGL(1,𝔽5)
socleC5×C7×C11C3×AGL(1,𝔽5)
prime radicalC11×ΓL(1,𝔽8)×D25C2
cosocleC7×C11×D25C2×C3
LCSG ▷ C7×C11×C25
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1925

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 56);