Finite Group Databasebeta

C2×C4×#14555487 #31783120

order17536
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×#14555487

Splittings

FittingC22×C42×C137 ⋊ C2
SylowC137 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D137
commutatorC2×C137C22×C42
FrattiniC23C23×D137
FittingC22×C42×C137C2
socleC24×C137C23
prime radicalC24×D137C22
cosocleC23×C137C24
hypercenterC22×C42D137
hypocenterC137C2×C4×C22⋊C4
LCSG ▷ C2×C137 ▷ C137
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8768

Conjugacy classes & character table

4432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17536, 6841);