Finite Group Databasebeta

C25×C29×C22⋊C9 #39907795

order26100
automorphism?
homologyAbelianization (H1) = C9×C25×C29 · Schur multiplier (H2) = C2

Aliases

direct productC25×C29×C22⋊C9
unambiguous semidirect productC22⋊(C9×C25×C29)
unambiguous semidirect product(C22×C25)⋊(C9×C29)
unambiguous semidirect product(C22×C29)⋊(C9×C25)
unambiguous semidirect product(C22×C25×C29)⋊C9

Splittings

derived, SylowC22 ⋊ C9×C25×C29
HallC22×C25×C29 ⋊ C9
HallC22×C29 ⋊ C9×C25
HallC22×C25 ⋊ C9×C29

Subgroups

subgroupG/H
center, hypercenterC3×C25×C29A4
commutator, hypocenterC22C9×C25×C29
FrattiniC3×C5C5×A4×C29
FittingC22×C3×C25×C29C3
socle, prime radicalC22×C3×C5×C29C3×C5
cosocleC22×C3×C5C3×C5×C29
LCSG ▷ C22
UCSC1 ◁ C3×C25×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13050

Conjugacy classes & character table

8700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 29);