Finite Group Databasebeta

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C2×C5×#4550 #14294271

order1920
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C2×C4×C5×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×C5×#4550

Splittings

HallC3×C5 ⋊ C2×#336
SylowC3 ⋊ C2×C5×#336

Subgroups

subgroupG/H
centerC23×C4×C5C2×D3
commutatorC2×C3C2×C4×C5×C8
FrattiniC22×C4C22×C5×D3
FittingC23×C3×C5×C8C2
socle, prime radicalC24×C3×C5C2×C4
cosocleC22×C3×C4C23×C5
hypercenterC23×C5×C8D3
hypocenterC3C2×C5×#336
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C4×C5 ◁ C23×C5×C8

1056 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, 19969);