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C52×C11×C22⋊ΓL(1,𝔽8) #37528733

order23100
automorphism?
homologyAbelianization (H1) = C3×C52×C11 · Schur multiplier (H2) = C2×C5

Aliases

direct productC52×C11×C22⋊ΓL(1,𝔽8)
unambiguous semidirect productC22⋊(C52×C11×ΓL(1,𝔽8))
unambiguous semidirect productC7⋊(C52×C11×A4)
unambiguous semidirect product(C22×C5)⋊(C5×C11×ΓL(1,𝔽8))
unambiguous semidirect product(C5×C7)⋊(C5×C11×A4)

Splittings

Fitting, socle, HallC22×C52×C7×C11 ⋊ C3
derived, HallC22×C7 ⋊ C3×C52×C11
HallC52×C7×C11 ⋊ A4
HallC22×C52×C11 ⋊ ΓL(1,𝔽8)
HallC22×C52×C7 ⋊ C3×C11
HallC22×C7×C11 ⋊ C3×C52
HallC52×C7 ⋊ C11×A4
HallC22×C52 ⋊ C11×ΓL(1,𝔽8)
HallC7×C11 ⋊ C52×A4
HallC22×C11 ⋊ C52×ΓL(1,𝔽8)
SylowC7 ⋊ C52×C11×A4
SylowC22 ⋊ C52×C11×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC52×C11C22⋊ΓL(1,𝔽8)
commutator, cosocle, hypocenterC22×C7C3×C52×C11
FrattiniC1G
Fitting, socleC22×C52×C7×C11C3
LCSG ▷ C22×C7
UCSC1 ◁ C52×C11

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7700

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 544);