Finite Group Databasebeta

C2×C7×C4⋊(C3⋊C8) #13055958

order1344
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C22×C7×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×C7×C4⋊(C3⋊C8)

Splittings

HallC3×C7 ⋊ C2×C4⋊C8
SylowC3 ⋊ C2×C7×C4⋊C8

Subgroups

subgroupG/H
centerC22×C4×C7C2×D3
commutatorC2×C3C22×C7×C8
FrattiniC2×C4C22×D3×C7
FittingC2×C3×C42×C7C2
socle, prime radicalC23×C3×C7C2×C4
cosocleC2×C3×C4C23×C7
hypercenterC2×C42×C7D3
hypocenterC3C2×C7×C4⋊C8
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C4×C7 ◁ C2×C42×C7

276 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1344

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 5247);