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C11×#1039⋊ΓL(1,𝔽8) #37528371

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

Aliases

direct productC11×#1039⋊ΓL(1,𝔽8)
unambiguous semidirect product#1039⋊(C11×ΓL(1,𝔽8))
unambiguous semidirect product(C11×#1039)⋊ΓL(1,𝔽8)

Splittings

derived, HallC52×C7 ⋊ C3×C4×C11
HallC7×C11×#1039 ⋊ C3
HallC11×C7⋊(C52⋊C3) ⋊ C4
HallC52×C7×C11 ⋊ C3×C4
HallC11×#1039 ⋊ ΓL(1,𝔽8)
HallC7×#1039 ⋊ C3×C11
HallC7⋊(C52⋊C3) ⋊ C4×C11
HallC52×C11 ⋊ C4×ΓL(1,𝔽8)
Hall#1039 ⋊ C11×ΓL(1,𝔽8)
HallC7×C11 ⋊ #1039⋊C3
SylowC52 ⋊ C4×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C11×#1039⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C11(C5⋊D5)⋊ΓL(1,𝔽8)
commutator, hypocenterC52×C7C3×C4×C11
FrattiniC2C11×(C5⋊D5)⋊ΓL(1,𝔽8)
Fitting, socleC2×C52×C7×C11C2×C3
prime radicalC2×C11×C7⋊(C52⋊C3)C2
cosocleC2×C52×C7C2×C3×C11
LCSG ▷ C52×C7
UCSC1 ◁ C2×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 182);