Finite Group Databasebeta

Q8⋊C16×D71 #31907249

order18176
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productQ8⋊C16×D71

Splittings

FittingC71×Q8⋊C16 ⋊ C2
SylowC71 ⋊ C2×Q8⋊C16

Subgroups

subgroupG/H
centerC2×C8D4×D71
commutatorC4×C71C22×C16
FrattiniC4×C8C22×D71
FittingC71×Q8⋊C16C2
socleC22×C71C2×C22⋊C8
prime radicalC22×D71C22⋊C8
cosocleC4×C8×C71C23
hypercenterQ8⋊C16D71
hypocenterC71C2×Q8⋊C16
LCSG ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C8 ◁ C4×C8 ◁ Q8⋊C16

382 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

2072 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 79365);