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C22×C5×ΓL(1,𝔽8)×C11⋊C5 #37528472

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC22×C5×ΓL(1,𝔽8)×C11⋊C5
unambiguous semidirect product(C22×C11×ΓL(1,𝔽8))⋊C52
unambiguous semidirect product(C22×C5×C11×ΓL(1,𝔽8))⋊C5

Splittings

Fitting, socleC22×C5×C7×C11 ⋊ C3×C5
derived, HallC7×C11 ⋊ C22×C3×C52
HallC22×C5×C7×C11⋊C5 ⋊ C3
HallC5×C7×C11⋊C5 ⋊ C22×C3
HallC22×C11×ΓL(1,𝔽8) ⋊ C52
HallC22×C7×C11 ⋊ C3×C52
HallC11×ΓL(1,𝔽8) ⋊ C22×C52
HallC22×C11 ⋊ C52×ΓL(1,𝔽8)
HallC22×C7 ⋊ C3×C5×C11⋊C5
SylowC11 ⋊ C22×C52×ΓL(1,𝔽8)
SylowC7 ⋊ C22×C3×C5×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC22×C5ΓL(1,𝔽8)×C11⋊C5
commutator, cosocle, hypocenterC7×C11C22×C3×C52
FrattiniC1G
Fitting, socleC22×C5×C7×C11C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C22×C5

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1540

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 283);