Finite Group Databasebeta

C22×#89461 #14217186

order1792
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×#89461

Splittings

FittingC22×C4×C7×C8 ⋊ C2
SylowC7 ⋊ C22×#405

Subgroups

subgroupG/H
centerC23×C8C2×D7
commutatorC2×C7C23×C42
FrattiniC2×C4C24×D7
FittingC22×C4×C7×C8C2
socleC24×C7C22×C4
prime radicalC24×D7C2×C4
cosocleC2×C4×C7C25
hypercenterC22×C4×C8D7
hypocenterC7C22×#405
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C23×C8 ◁ C22×C4×C8

3518 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1032958);