Finite Group Databasebeta

#117×C22⋊D7 #13513196

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct product#117×C22⋊D7

Splittings

FittingC22×C7×#117 ⋊ C2
SylowC7 ⋊ D4×#117

Subgroups

subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC22×C7×#117C2
socle, cosocleC23×C7C25
prime radicalC23×C22⋊D7C22
hypercenterC22×#117D7
hypocenterC7D4×#117
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C22×#117

3562 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, 328968);