Finite Group Databasebeta

#468×D167 #36333722

order21376
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct product#468×D167

Splittings

Fitting#468×C167 ⋊ C2
SylowC167 ⋊ C2×#468

Subgroups

subgroupG/H
centerC22C2×D4×D167
commutator, cosocleC2×C4×C167C24
FrattiniC2×C4C23×D167
Fitting#468×C167C2
socleC22×C167C22×D4
prime radical#121×D167C2
hypercenter#468D167
hypocenterC167C2×#468
LCSG ▷ C2×C4×C167 ▷ C2×C167 ▷ C167
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5344

Conjugacy classes & character table

1360 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 14094);