Finite Group Databasebeta

D8×#11765848 #31968869

order18176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD8×#11765848

Splittings

FittingC8×D8×C71 ⋊ C2
SylowC71 ⋊ M16×D8

Subgroups

subgroupG/H
centerC2×C4C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC42C23×D71
FittingC8×D8×C71C2
socleC22×C71C2×C4×D4
prime radicalC2×D8×D71C4
cosocleC42×C71C24
hypercenterC8×D8D71
hypocenterC71M16×D8
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D8

794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

2030 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 140985);