Finite Group Databasebeta

C22×Q8×C22⋊D53 #28291006

order13568
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C214

Aliases

direct productC22×Q8×C22⋊D53

Splittings

FittingC24×Q8×C53 ⋊ C2
SylowC53 ⋊ C22×D4×Q8

Subgroups

subgroupG/H
centerC24C23×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC24×Q8×C53C2
socleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC24×Q8D53
hypocenterC53C22×D4×Q8
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C24×Q8

11798 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6784

Conjugacy classes & character table

2180 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1076482);