Finite Group Databasebeta

C2×C3×Dic7⋊C8 #13055532

order1344
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C22×C3×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×C3×Dic7⋊C8

Splittings

HallC3×C7 ⋊ C2×C4⋊C8
SylowC7 ⋊ C2×C3×C4⋊C8

Subgroups

subgroupG/H
centerC22×C3×C4C2×D7
commutatorC2×C7C22×C3×C8
FrattiniC2×C4C22×C3×D7
FittingC22×C3×C7×C8C2
socle, prime radicalC23×C3×C7C2×C4
cosocleC2×C4×C7C23×C3
hypercenterC22×C3×C8D7
hypocenterC7C2×C3×C4⋊C8
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C3×C4 ◁ C22×C3×C8

276 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1344

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 4821);