Finite Group Databasebeta

C2×C4×#6470 #14217201

order1792
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×C4×#6470

Splittings

FittingC2×C4×C7×M16 ⋊ C2
SylowC7 ⋊ C2×C4×#131

Subgroups

subgroupG/H
centerC2×C42C22×D7
commutatorC2×C7C23×C42
FrattiniC2×C4C24×D7
FittingC2×C4×C7×M16C2
socleC23×C7C23×C4
prime radicalC22×#1157C22
cosocleC2×C4×C7C25
hypercenterC2×C4×M16D7
hypocenterC7C2×C4×#131
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C42 ◁ C2×C4×M16

3366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 896

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1032973);