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C11×ΓL(1,𝔽8)⋊#1043 #37528546

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

Aliases

direct productC11×ΓL(1,𝔽8)⋊#1043
unambiguous semidirect productΓL(1,𝔽8)⋊(C11×#1043)

Splittings

Fitting, socle, HallC52×C7×C11 ⋊ C3×C4
derived, HallC52×C7 ⋊ C3×C4×C11
HallC11×C7⋊#1043 ⋊ C3
HallC52×C11×ΓL(1,𝔽8) ⋊ C4
HallC7⋊#1043 ⋊ C3×C11
HallC52×ΓL(1,𝔽8) ⋊ C4×C11
HallC52×C11 ⋊ ΓL(1,𝔽8)⋊C4
HallC11×ΓL(1,𝔽8) ⋊ #1043
HallC7×C11 ⋊ C3×#1043
SylowC52 ⋊ C11×ΓL(1,𝔽8)⋊C4
HallΓL(1,𝔽8) ⋊ C11×#1043
SylowC7 ⋊ C3×C11×#1043

Subgroups

subgroupG/H
center, hypercenterC11ΓL(1,𝔽8)⋊#1043
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

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1925

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 357);