Finite Group Databasebeta

C2×M16×C22⋊D53 #28247991

order13568
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×M16×C22⋊D53

Splittings

FittingC23×M16×C53 ⋊ C2
SylowC53 ⋊ C2×D4×M16

Subgroups

subgroupG/H
centerC22×C4C23×D53
commutatorC22×C53C24×C4
FrattiniC2×C4C24×D53
FittingC23×M16×C53C2
socleC23×C53C23×C4
prime radicalC23×C22⋊D53C4
cosocleC2×C4×C53C25
hypercenterC23×M16D53
hypocenterC53C2×D4×M16
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C23×M16

3218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

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, 1033467);