Finite Group Databasebeta

← Prev (#37557149) Next (#37557151) →

C25×C22⋊(C79⋊C3) #37557150

order23700
automorphism?
homologyAbelianization (H1) = C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC25×C22⋊(C79⋊C3)
unambiguous semidirect productC22⋊(C25×C79⋊C3)
unambiguous semidirect productC79⋊(A4×C25)
unambiguous semidirect product(C22×C25)⋊(C79⋊C3)
unambiguous semidirect product(C25×C79)⋊A4

Splittings

Fitting, HallC22×C25×C79 ⋊ C3
derived, HallC22×C79 ⋊ C3×C25
HallC25×C79 ⋊ A4
HallC22×C25 ⋊ C79⋊C3
SylowC79 ⋊ A4×C25
SylowC22 ⋊ C25×C79⋊C3

Subgroups

subgroupG/H
center, hypercenterC25C22⋊(C79⋊C3)
commutator, hypocenterC22×C79C3×C25
FrattiniC5C5×C22⋊(C79⋊C3)
FittingC22×C25×C79C3
socle, cosocleC22×C5×C79C3×C5
prime radicalC5×C22⋊(C79⋊C3)C5
LCSG ▷ C22×C79
UCSC1 ◁ C25

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7900

Conjugacy classes & character table

2700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23700, 33);