Finite Group Databasebeta

C4×D7×#124 #13512263

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

Aliases

direct productC4×D7×#124

Splittings

FittingC4×C7×#124 ⋊ C2
SylowC7 ⋊ C2×C4×#124

Subgroups

subgroupG/H
centerC22×C4C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC4×C7×#124C2
socle, cosocleC23×C7C25
prime radicalC22×D4×D7C22
hypercenterC4×#124D7
hypocenterC7C2×C4×#124
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C4×#124

3790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 328035);