Finite Group Databasebeta

← Prev (#13055400) Next (#13055402) →

C3×C4⋊C4×Dic7 #13055401

order1344
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC3×C4⋊C4×Dic7

Splittings

HallC3×C7 ⋊ C4×C4⋊C4
SylowC7 ⋊ C3×C4×C4⋊C4

Subgroups

subgroupG/H
centerC23×C3C22×D7
commutatorC2×C7C2×C3×C42
FrattiniC23C22×C3×D7
FittingC2×C3×C7×C4⋊C4C2
socle, prime radicalC23×C3×C7C23
cosocleC23×C7C23×C3
hypercenterC2×C3×C4⋊C4D7
hypocenterC7C3×C4×C4⋊C4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C23×C3 ◁ C2×C3×C4⋊C4

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1344

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4690);