Finite Group Databasebeta

C2×C4×D7×D8 #14217794

order1792
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×C4×D7×D8

Splittings

FittingC2×C4×C7×D8 ⋊ C2
SylowC7 ⋊ C22×C4×D8

Subgroups

subgroupG/H
centerC22×C4D4×D7
commutatorC4×C7C24×C4
FrattiniC2×C4C24×D7
FittingC2×C4×C7×D8C2
socleC23×C7C22×D4
prime radicalC22×D7×D8C2
cosocleC2×C4×C7C25
hypercenterC2×C4×D8D7
hypocenterC7C22×C4×D8
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×D8

3694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 448

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1792, 1033566);