Finite Group Databasebeta

C2×Q16×C22⋊D53 #28259363

order13568
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×Q16×C22⋊D53

Splittings

FittingC23×Q16×C53 ⋊ C2
SylowC53 ⋊ C2×D4×Q16

Subgroups

subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC23×Q16×C53C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
hypercenterC23×Q16D53
hypocenterC53C2×D4×Q16
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×Q16

2742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6784

Conjugacy classes & character table

1526 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1044839);