Finite Group Databasebeta

C7×Dic3×C4⋊C4 #13056003

order1344
automorphism?
homologyAbelianization (H1) = C2×C42×C7 · Schur multiplier (H2) = C22×C4

Aliases

direct productC7×Dic3×C4⋊C4

Splittings

HallC3×C7 ⋊ C4×C4⋊C4
SylowC3 ⋊ C4×C7×C4⋊C4

Subgroups

subgroupG/H
centerC23×C7C22×D3
commutatorC2×C3C2×C42×C7
FrattiniC23C22×D3×C7
FittingC2×C3×C7×C4⋊C4C2
socle, prime radicalC23×C3×C7C23
cosocleC23×C3C23×C7
hypercenterC2×C7×C4⋊C4D3
hypocenterC3C4×C7×C4⋊C4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C7 ◁ C2×C7×C4⋊C4

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1344

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, 5292);