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C2×C5×#1143 #11765101

order1120
isoclinismisoclinic class of #1141
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C22

Aliases

direct productC2×C5×#1143

Splittings

FittingC2×C5×C7×Q8 ⋊ C2
HallC5×C7 ⋊ C2×SD16
SylowC7 ⋊ C2×C5×SD16

Subgroups

subgroupG/H
centerC22×C5C22⋊D7
commutator, cosocleC4×C7C23×C5
FrattiniC4C22×C5×D7
FittingC2×C5×C7×Q8C2
socleC22×C5×C7D4
prime radicalC2×C5×D28C2
hypercenterC2×C5×Q8D7
hypocenterC7C2×C5×SD16
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C2×C5×Q8

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 560

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 707);