Finite Group Databasebeta

C3×C4×C8×Dic5 #14294183

order1920
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C3×C42×C8 · Schur multiplier (H2) = C43

Aliases

direct productC3×C4×C8×Dic5

Splittings

derived, SylowC5 ⋊ C3×C42×C8
HallC3×C5 ⋊ C42×C8

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4×C8D5
commutator, hypocenterC5C3×C42×C8
FrattiniC22×C4C22×C3×D5
FittingC2×C3×C4×C5×C8C2
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×C4×C5C23×C3
LCSG ▷ C5
UCSC1 ◁ C2×C3×C4×C8

816 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 19881);