Finite Group Databasebeta

C22×#89774 #14217312

order1792
isoclinismisoclinic class of #1141
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#89774

Splittings

FittingC22×C7×#117 ⋊ C2
SylowC7 ⋊ C22×#416

Subgroups

subgroupG/H
centerC23×C4C22⋊D7
commutatorC4×C7C24×C4
FrattiniC2×C4C24×D7
FittingC22×C7×#117C2
socleC24×C7C2×D4
prime radicalC23×#1157C2
cosocleC2×C4×C7C25
hypercenterC22×#117D7
hypocenterC7C22×#416
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C23×C4 ◁ C24×C4 ◁ C22×#117

5326 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, 1033084);