Finite Group Databasebeta

C2×C4×#6435 #13511982

order1792
isoclinismisoclinic class of Dic14
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C27×C42

Aliases

direct productC2×C4×#6435

Splittings

FittingC2×C43×C7 ⋊ C2
SylowC7 ⋊ C2×C4×#117

Subgroups

subgroupG/H
centerC22×C42C2×D7
commutatorC2×C7C23×C42
FrattiniC23C24×D7
FittingC2×C43×C7C2
socleC24×C7C24
prime radicalC24×D7C23
cosocleC23×C7C25
hypercenterC2×C43D7
hypocenterC7C2×C4×#117
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C42 ◁ C2×C43

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 327754);