Finite Group Databasebeta

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C7×C11×A4×C25 #37528311

order23100
automorphism?
homologyAbelianization (H1) = C3×C7×C11×C25 · Schur multiplier (H2) = C2

Aliases

direct productC7×C11×A4×C25
unambiguous semidirect productC22⋊(C3×C7×C11×C25)
unambiguous semidirect product(C22×C25)⋊(C3×C7×C11)
unambiguous semidirect product(C22×C11×C25)⋊(C3×C7)

Splittings

Fitting, HallC22×C7×C11×C25 ⋊ C3
derived, SylowC22 ⋊ C3×C7×C11×C25
HallC22×C11×C25 ⋊ C3×C7
HallC22×C7×C25 ⋊ C3×C11
HallC22×C7×C11 ⋊ C3×C25
HallC22×C25 ⋊ C3×C7×C11
HallC22×C11 ⋊ C3×C7×C25
HallC22×C7 ⋊ C3×C11×C25

Subgroups

subgroupG/H
center, hypercenterC7×C11×C25A4
commutator, hypocenterC22C3×C7×C11×C25
FrattiniC5C5×C7×C11×A4
FittingC22×C7×C11×C25C3
socleC22×C5×C7×C11C3×C5
prime radicalC5×C7×C11×A4C5
cosocleC22×C5C3×C5×C7×C11
LCSG ▷ C22
UCSC1 ◁ C7×C11×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7700

Conjugacy classes & character table

7700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 122);