Finite Group Databasebeta

C2×D7×#390 #13512145

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210×C4

Aliases

direct productC2×D7×#390

Splittings

FittingC2×C7×#390 ⋊ C2
SylowC7 ⋊ C22×#390

Subgroups

subgroupG/H
centerC24C23×D7
commutatorC22×C7C24×C4
FrattiniC23C24×D7
FittingC2×C7×#390C2
socleC24×C7C24
prime radicalC23×D4×D7C2
cosocleC23×C7C25
hypercenterC2×#390D7
hypocenterC7C22×#390
LCSG ▷ C22×C7 ▷ C7
UCSC1 ◁ C24 ◁ C2×#390

9534 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, 327917);