Finite Group Databasebeta

← Prev (#14411159) Next (#14411161) →

C22×C5×C8×Dic3 #14411160

order1920
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C22×C4×C5×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×C5×C8×Dic3

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC23×C5×C8D3
commutator, hypocenterC3C22×C4×C5×C8
FrattiniC2×C4C23×C5×D3
FittingC23×C3×C5×C8C2
socle, prime radicalC24×C3×C5C2×C4
cosocleC2×C3×C4C24×C5
LCSG ▷ C3
UCSC1 ◁ C23×C5×C8

1520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 136858);