Finite Group Databasebeta

C4×D7×#117 #13511977

order1792
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C27×C42

Aliases

direct productC4×D7×#117

Splittings

FittingC4×C7×#117 ⋊ C2
SylowC7 ⋊ C2×C4×#117

Subgroups

subgroupG/H
centerC2×C42C22×D7
commutatorC2×C7C23×C42
FrattiniC23C24×D7
FittingC4×C7×#117C2
socle, cosocleC23×C7C25
prime radicalC24×D7C23
hypercenterC4×#117D7
hypocenterC7C2×C4×#117
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C42 ◁ C4×#117

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 327749);