Finite Group Databasebeta

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C2×C5×D56 #11765061

order1120
isoclinismisoclinic class of #1132
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C23

Aliases

direct productC2×C5×D56

Splittings

FittingC2×C5×C7×C8 ⋊ C2
HallC5×C7 ⋊ C2×D8
SylowC7 ⋊ C2×C5×D8

Subgroups

subgroupG/H
centerC22×C5D28
commutator, cosocleC4×C7C23×C5
FrattiniC4C22×C5×D7
FittingC2×C5×C7×C8C2
socleC22×C5×C7D4
hypercenterC2×C5×C8D7
hypocenterC7C2×C5×D8
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C2×C5×C8

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 560

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 667);