Finite Group Databasebeta

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C2×C5×#1136 #11765079

order1120
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22

Aliases

direct productC2×C5×#1136

Splittings

HallC5×C7 ⋊ C2×M16
SylowC7 ⋊ C2×C5×M16

Subgroups

subgroupG/H
centerC2×C4×C5C2×D7
commutatorC2×C7C22×C4×C5
FrattiniC4C22×C5×D7
FittingC22×C4×C5×C7C2
socleC22×C5×C7C2×C4
prime radicalC23×C5×C7C4
cosocleC4×C7C23×C5
hypercenterC22×C4×C5D7
hypocenterC7C2×C5×M16
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4×C5 ◁ C22×C4×C5

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 560

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 685);