Finite Group Databasebeta

C2×D4×#11719924 #28259308

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

Aliases

direct productC2×D4×#11719924

Splittings

FittingC2×D4×Q8×C53 ⋊ C2
SylowC53 ⋊ C2×D4×SD16

Subgroups

subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×D4×Q8×C53C2
socleC23×C53C22×D4
prime radicalC2×D4×D212C2
hypercenterC2×D4×Q8D53
hypocenterC53C2×D4×SD16
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

3226 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

Conjugacy classes & character table

1370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1044784);