Finite Group Databasebeta

C2×C3×C4×#681 #14411236

order1920
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C22×C3×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×C3×C4×#681

Splittings

HallC3×C5 ⋊ C2×C4×M16
SylowC5 ⋊ C2×C3×C4×M16

Subgroups

subgroupG/H
centerC2×C3×C42C2×D5
commutatorC2×C5C22×C3×C42
FrattiniC2×C4C23×C3×D5
FittingC22×C3×C42×C5C2
socleC23×C3×C5C22×C4
prime radicalC24×C3×C5C2×C4
cosocleC2×C4×C5C24×C3
hypercenterC22×C3×C42D5
hypocenterC5C2×C3×C4×M16
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C42 ◁ C22×C3×C42

1312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 136934);