Finite Group Databasebeta

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C5×C7×A4×C11⋊C5 #37528470

order23100
automorphism?
homologyAbelianization (H1) = C3×C52×C7 · Schur multiplier (H2) = C2×C5

Aliases

direct productC5×C7×A4×C11⋊C5
unambiguous semidirect productC22⋊(C3×C5×C7×C11⋊C5)
unambiguous semidirect productC11⋊(C52×C7×A4)
unambiguous semidirect product(C22×C5)⋊(C3×C7×C11⋊C5)
unambiguous semidirect product(C5×C11)⋊(C5×C7×A4)
unambiguous semidirect product(C11×A4)⋊(C52×C7)
unambiguous semidirect product(C22×C11⋊C5)⋊(C3×C5×C7)
unambiguous semidirect product(C5×C11×A4)⋊(C5×C7)
unambiguous semidirect product(C7×C11×A4)⋊C52
unambiguous semidirect product(C22×C5×C11⋊C5)⋊(C3×C7)
unambiguous semidirect product(C5×C7×C11×A4)⋊C5

Splittings

Fitting, socleC22×C5×C7×C11 ⋊ C3×C5
derived, HallC22×C11 ⋊ C3×C52×C7
HallC22×C5×C7×C11⋊C5 ⋊ C3
HallC22×C5×C11⋊C5 ⋊ C3×C7
HallC7×C11×A4 ⋊ C52
HallC22×C7×C11 ⋊ C3×C52
HallC11×A4 ⋊ C52×C7
HallC7×C11 ⋊ C52×A4
HallC22×C7 ⋊ C3×C5×C11⋊C5
SylowC11 ⋊ C52×C7×A4
SylowC22 ⋊ C3×C5×C7×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC5×C7A4×C11⋊C5
commutator, cosocle, hypocenterC22×C11C3×C52×C7
FrattiniC1G
Fitting, socleC22×C5×C7×C11C3×C5
LCSG ▷ C22×C11
UCSC1 ◁ C5×C7

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1540

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 281);