Finite Group Databasebeta

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C7×A4×C11⋊C25 #37528239

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

Aliases

direct productC7×A4×C11⋊C25
unambiguous semidirect productC22⋊(C3×C7×C11⋊C25)
unambiguous semidirect productC11⋊(C7×A4×C25)
unambiguous semidirect product(C11×A4)⋊(C7×C25)
unambiguous semidirect product(C7×C11×A4)⋊C25
unambiguous semidirect product(C22×C11⋊C25)⋊(C3×C7)

Splittings

derived, HallC22×C11 ⋊ C3×C7×C25
HallC22×C7×C11⋊C25 ⋊ C3
HallC22×C11⋊C25 ⋊ C3×C7
HallC7×C11×A4 ⋊ C25
HallC22×C7×C11 ⋊ C3×C25
HallC11×A4 ⋊ C7×C25
HallC7×C11 ⋊ A4×C25
HallC22×C7 ⋊ C3×C11⋊C25
SylowC11 ⋊ C7×A4×C25
SylowC22 ⋊ C3×C7×C11⋊C25

Subgroups

subgroupG/H
center, hypercenterC5×C7A4×C11⋊C5
commutator, hypocenterC22×C11C3×C7×C25
FrattiniC5C7×A4×C11⋊C5
Fitting, socleC22×C5×C7×C11C3×C5
prime radicalC5×C7×C11×A4C5
cosocleC22×C5×C11C3×C5×C7
LCSG ▷ C22×C11
UCSC1 ◁ C5×C7

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7700

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, 50);