Finite Group Databasebeta

C22×#89278 #13320137

order1792
isoclinismisoclinic class of #1141
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC22×#89278

Splittings

FittingC22×C7×C4⋊C8 ⋊ C2
SylowC7 ⋊ C22×D4⋊C8

Subgroups

subgroupG/H
centerC23×C4C22⋊D7
commutatorC4×C7C23×C8
FrattiniC42C23×D7
FittingC22×C7×C4⋊C8C2
socleC24×C7C22⋊C4
prime radicalC23×D28C4
cosocleC42×C7C24
hypercenterC22×C4⋊C8D7
hypocenterC7C22×D4⋊C8
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4⋊C8

1886 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, 135909);