Finite Group Databasebeta

Q8×#14556044 #32014011

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

Aliases

direct productQ8×#14556044

Splittings

FittingQ8×M16×C71 ⋊ C2
SylowC71 ⋊ Q8×#100

Subgroups

subgroupG/H
centerC22C22×(C2×D71)⋊C4
commutatorC23×C71C23×C4
FrattiniC22×C4C23×D71
FittingQ8×M16×C71C2
socleC22×C71C22×C22⋊C4
prime radicalC22×D284C23
cosocleC22×C4×C71C24
hypercenterQ8×M16D71
hypocenterC71Q8×#100
LCSG ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C4×Q8 ◁ Q8×M16

1198 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4544

Conjugacy classes & character table

1805 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 186127);