Finite Group Databasebeta

C2×C7×#924 #13061500

order1344
automorphism?
homologyAbelianization (H1) = C24×C7 · Schur multiplier (H2) = C25

Aliases

direct productC2×C7×#924

Splittings

HallC3×C7 ⋊ C2×C22⋊Q8
SylowC3 ⋊ C2×C7×C22⋊Q8

Subgroups

subgroupG/H
centerC23×C7C22×D3
commutator, cosocleC22×C3C24×C7
FrattiniC22C23×D3×C7
FittingC23×C3×C4×C7C2
socleC23×C3×C7C23
prime radicalC24×C3×C7C22
hypercenterC23×C4×C7D3
hypocenterC3C2×C7×C22⋊Q8
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C7 ◁ C23×C4×C7

644 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 672

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 10789);