Finite Group Databasebeta

C22×#90186 #14260772

order1792
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC22×#90186

Splittings

FittingC23×C7×C22⋊C4 ⋊ C2
SylowC7 ⋊ C22×#551

Subgroups

subgroupG/H
centerC24C23×D7
commutator, cosocleC22×C7C26
FrattiniC22C25×D7
FittingC23×C7×C22⋊C4C2
socleC24×C7C24
prime radicalC22×#6516C2
hypercenterC23×C22⋊C4D7
hypocenterC7C22×#551
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C23×C22⋊C4

9526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1076544);