Finite Group Databasebeta

#399×Dic71 #31919283

order18176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#399×Dic71

Splittings

SylowC71 ⋊ C4×#399

Subgroups

subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC2×#399×C71C2
socle, cosocleC24×C71C24
prime radicalC25×C71C23
hypercenterC2×#399D71
hypocenterC71C4×#399
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#399

1966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9088

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 91399);