Finite Group Databasebeta

← Prev (#14416142) Next (#14416144) →

C2×C3×C4×#689 #14416143

order1920
isoclinismisoclinic class of #686
automorphism?
homologyAbelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×C3×C4×#689

Splittings

HallC3×C5 ⋊ C2×C4×Q16
SylowC5 ⋊ C2×C3×C4×Q16

Subgroups

subgroupG/H
centerC22×C3×C4C22⋊D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC2×C3×C4×C5×Q8C2
socle, prime radicalC23×C3×C5C2×D4
cosocleC2×C4×C5C24×C3
hypercenterC2×C3×C4×Q8D5
hypocenterC5C2×C3×C4×Q16
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C42 ◁ C2×C3×C4×Q8

976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 141841);