Finite Group Databasebeta

C2×#20290428 #28318005

order13568
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C42

Aliases

direct productC2×#20290428

Splittings

FittingC2×C4×C8×C53 ⋊ C4
SylowC53 ⋊ C2×#1744

Subgroups

subgroupG/H
centerC2×C42C2×#6157
commutatorC2×C53C22×C4×C8
FrattiniC2×C4C23×#6157
FittingC2×C4×C8×C53C4
socleC23×C53C2×C42
prime radicalC23×D53C22×C4
cosocleC2×C4×D53C24
hypercenterC2×C4×C8#6157
hypocenterC53C2×#1744
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C42 ◁ C2×C4×C8

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1103481);