Finite Group Databasebeta

C2×C8×D4×D7 #14217624

order1792
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C210

Aliases

direct productC2×C8×D4×D7

Splittings

FittingC2×C7×C8×D4 ⋊ C2
SylowC7 ⋊ C22×C8×D4

Subgroups

subgroupG/H
centerC22×C8C22×D7
commutatorC2×C7C24×C8
FrattiniC2×C4C24×D7
FittingC2×C7×C8×D4C2
socleC23×C7C23×C4
prime radicalC22×D4×D7C4
cosocleC2×C4×C7C25
hypercenterC2×C8×D4D7
hypocenterC7C22×C8×D4
LCSG ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C8 ◁ C2×C8×D4

3694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

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, 1033396);