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C2×C11×(C5⋊D5)⋊ΓL(1,𝔽8) #37528583

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C11×(C5⋊D5)⋊ΓL(1,𝔽8)
unambiguous semidirect product(C2×C5⋊D5)⋊(C11×ΓL(1,𝔽8))
unambiguous semidirect product(C2×C11×C5⋊D5)⋊ΓL(1,𝔽8)

Splittings

Fitting, socleC2×C52×C7×C11 ⋊ C2×C3
derived, HallC52×C7 ⋊ C22×C3×C11
HallC2×C7×C11×C5⋊D5 ⋊ C3
HallC11×C7⋊(C52⋊C3) ⋊ C22
HallC52×C7×C11 ⋊ C22×C3
HallC2×C11×C5⋊D5 ⋊ ΓL(1,𝔽8)
HallC2×C7×C5⋊D5 ⋊ C3×C11
HallC7⋊(C52⋊C3) ⋊ C22×C11
HallC52×C11 ⋊ C22×ΓL(1,𝔽8)
HallC2×C5⋊D5 ⋊ C11×ΓL(1,𝔽8)
HallC7×C11 ⋊ C2×(C5⋊D5)⋊C3
SylowC52 ⋊ C22×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C2×C11×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C11(C5⋊D5)⋊ΓL(1,𝔽8)
commutator, cosocle, hypocenterC52×C7C22×C3×C11
FrattiniC1G
Fitting, socleC2×C52×C7×C11C2×C3
LCSG ▷ C52×C7
UCSC1 ◁ C2×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

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, 394);