Finite Group Databasebeta

C23×C22⋊#88322 #28247519

order13568
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C211

Aliases

direct productC23×C22⋊#88322

Splittings

SylowC53 ⋊ C23×C22⋊C8

Subgroups

subgroupG/H
centerC24×C4C2×D53
commutatorC2×C53C24×C8
FrattiniC2×C4C24×D53
FittingC25×C4×C53C2
socleC25×C53C2×C4
prime radicalC26×C53C4
cosocleC2×C4×C53C25
hypercenterC25×C4D53
hypocenterC53C23×C22⋊C8
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C24×C4 ◁ C25×C4

7646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6784

Conjugacy classes & character table

3488 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1032995);