Finite Group Databasebeta

C2×C7×C22⋊Dic5 #11765196

order1120
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C24

Aliases

direct productC2×C7×C22⋊Dic5

Splittings

HallC5×C7 ⋊ C2×C22⋊C4
SylowC5 ⋊ C2×C7×C22⋊C4

Subgroups

subgroupG/H
centerC23×C7C2×D5
commutatorC2×C5C22×C4×C7
FrattiniC22C22×C7×D5
Fitting, prime radicalC24×C5×C7C2
socleC23×C5×C7C22
cosocleC22×C5C23×C7
hypercenterC24×C7D5
hypocenterC5C2×C7×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C7 ◁ C24×C7

264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 560

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 802);