Finite Group Databasebeta

C22×Q8×C22⋊D5 #13006214

order1280
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×Q8×C22⋊D5

Splittings

FittingC24×C5×Q8 ⋊ C2
SylowC5 ⋊ C22×D4×Q8

Subgroups

subgroupG/H
centerC24C23×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC24×C5×Q8C2
socleC24×C5C24
prime radicalC23×C22⋊D5C22
hypercenterC24×Q8D5
hypocenterC5C22×D4×Q8
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C24×Q8

11798 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1076482);