Finite Group Databasebeta

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C2×C3×#64676 #14281521

order1920
isoclinismisoclinic class of #677
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×C3×#64676

Splittings

HallC3×C5 ⋊ C2×Q8⋊C8
SylowC5 ⋊ C2×C3×Q8⋊C8

Subgroups

subgroupG/H
centerC22×C3×C4D20
commutatorC4×C5C22×C3×C8
FrattiniC42C22×C3×D5
FittingC2×C3×C4×C5×C8C2
socle, prime radicalC23×C3×C5C22⋊C4
cosocleC42×C5C23×C3
hypercenterC2×C3×C4×C8D5
hypocenterC5C2×C3×Q8⋊C8
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C2×C3×C42 ◁ C2×C3×C4×C8

560 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1920

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 7219);