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C11×ΓL(1,𝔽8)×#1044 #37528552

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C5

Aliases

direct productC11×ΓL(1,𝔽8)×#1044
unambiguous semidirect product(C7×#1044)⋊(C3×C11)
unambiguous semidirect product(C7×C11×#1044)⋊C3

Splittings

Fitting, socle, HallC52×C7×C11 ⋊ C3×C4
derived, HallC52×C7 ⋊ C3×C4×C11
HallC7×C11×#1044 ⋊ C3
HallC52×C11×ΓL(1,𝔽8) ⋊ C4
HallC7×#1044 ⋊ C3×C11
HallC52×ΓL(1,𝔽8) ⋊ C4×C11
HallC52×C11 ⋊ C4×ΓL(1,𝔽8)
HallC7×C11 ⋊ C3×#1044
SylowC52 ⋊ C4×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C11×#1044

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)×#1044
commutator, hypocenterC52×C7C3×C4×C11
FrattiniC1G
Fitting, socleC52×C7×C11C3×C4
prime radicalC11×ΓL(1,𝔽8)×C5⋊D5C2
cosocleC7×C5⋊D5C2×C3×C11
LCSG ▷ C52×C7
UCSC1 ◁ C11

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 770

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, 363);