Finite Group Databasebeta

← Prev (#14511318) Next (#14511320) →

C4×C5×2−1+4⋊C3 #14511319

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC4×C5×2−1+4⋊C3
unambiguous semidirect product(C4×C5×2−1+4)⋊C3

Splittings

Fitting, HallC4×C5×2−1+4 ⋊ C3
SylowC4×2−1+4 ⋊ C3×C5

Subgroups

subgroupG/H
centerC2×C4×C5C22×A4
commutator, hypocenterQ8C22×C3×C4×C5
FrattiniC22C23×C5×A4
FittingC4×C5×2−1+4C3
socleC22×C5C23×A4
prime radicalC2×C5×2−1+4⋊C3C2
cosocleC2×Q8C23×C3×C5
hypercenterC4×C5×D4A4
LCSG ▷ Q8
UCSC1 ◁ C2×C4×C5 ◁ C4×C5×D4

744 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

380 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 237017);