Finite Group Databasebeta

C2×C5×C22⋊Dic7 #11765110

order1120
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC2×C5×C22⋊Dic7

Splittings

HallC5×C7 ⋊ C2×C22⋊C4
SylowC7 ⋊ C2×C5×C22⋊C4

Subgroups

subgroupG/H
centerC23×C5C2×D7
commutatorC2×C7C22×C4×C5
FrattiniC22C22×C5×D7
Fitting, prime radicalC24×C5×C7C2
socleC23×C5×C7C22
cosocleC22×C7C23×C5
hypercenterC24×C5D7
hypocenterC7C2×C5×C22⋊C4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C23×C5 ◁ C24×C5

264 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, 716);