Finite Group Databasebeta

C22×C5×C4⋊(C3⋊C8) #14412967

order1920
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C23×C5×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×C5×C4⋊(C3⋊C8)

Splittings

HallC3×C5 ⋊ C22×C4⋊C8
SylowC3 ⋊ C22×C5×C4⋊C8

Subgroups

subgroupG/H
centerC23×C4×C5C2×D3
commutatorC2×C3C23×C5×C8
FrattiniC2×C4C23×C5×D3
FittingC22×C3×C42×C5C2
socle, prime radicalC24×C3×C5C2×C4
cosocleC2×C3×C4C24×C5
hypercenterC22×C42×C5D3
hypocenterC3C22×C5×C4⋊C8
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C4×C5 ◁ C22×C42×C5

1280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 138665);