Finite Group Databasebeta

C23×C5×C4⋊Dic3 #14478706

order1920
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C24×C4×C5 · Schur multiplier (H2) = C210

Aliases

direct productC23×C5×C4⋊Dic3

Splittings

HallC3×C5 ⋊ C23×C4⋊C4
SylowC3 ⋊ C23×C5×C4⋊C4

Subgroups

subgroupG/H
centerC25×C5C2×D3
commutatorC2×C3C24×C4×C5
FrattiniC22C24×C5×D3
FittingC24×C3×C4×C5C2
socle, prime radicalC25×C3×C5C22
cosocleC22×C3C25×C5
hypercenterC24×C4×C5D3
hypocenterC3C23×C5×C4⋊C4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C25×C5 ◁ C24×C4×C5

4976 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, 204404);