Finite Group Databasebeta

#462×D167 #36333572

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

Aliases

direct product#462×D167

Splittings

Fitting#462×C167 ⋊ C2
SylowC167 ⋊ C2×#462

Subgroups

subgroupG/H
centerC22C2×D4×D167
commutator, cosocleC2×C4×C167C24
FrattiniC2×C4C23×D167
Fitting#462×C167C2
socleC22×C167C22×D4
prime radicalC22×D167C2×D4
hypercenter#462D167
hypocenterC167C2×#462
LCSG ▷ C2×C4×C167 ▷ C2×C167 ▷ C167
UCSC1 ◁ C22 ◁ C42 ◁ #462

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10688

Conjugacy classes & character table

1615 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 13944);