Finite Group Databasebeta

C2×C4×#6503 #13512308

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC2×C4×#6503

Splittings

FittingC22×C4×C7×D4 ⋊ C2
SylowC7 ⋊ C2×C4×#127

Subgroups

subgroupG/H
centerC23×C4C22×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC22×C4×C7×D4C2
socleC24×C7C24
prime radicalC22×#6503C2
cosocleC23×C7C25
hypercenterC22×C4×D4D7
hypocenterC7C2×C4×#127
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

5694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 328080);