Finite Group Databasebeta

← Prev (#38737606) Next (#38737608) →

C5×A4×C419 #38737607

order25140
automorphism?
homologyAbelianization (H1) = C3×C5×C419 · Schur multiplier (H2) = C2

Aliases

direct productC5×A4×C419
unambiguous semidirect productC22⋊(C3×C5×C419)
unambiguous semidirect product(C22×C5)⋊(C3×C419)
unambiguous semidirect product(C22×C419)⋊(C3×C5)
unambiguous semidirect product(C22×C5×C419)⋊C3

Splittings

Fitting, socle, HallC22×C5×C419 ⋊ C3
derived, SylowC22 ⋊ C3×C5×C419
HallC22×C419 ⋊ C3×C5
HallC22×C5 ⋊ C3×C419

Subgroups

subgroupG/H
center, hypercenterC5×C419A4
commutator, cosocle, hypocenterC22C3×C5×C419
FrattiniC1G
Fitting, socleC22×C5×C419C3
LCSG ▷ C22
UCSC1 ◁ C5×C419

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8380

Conjugacy classes & character table

8380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25140, 21);