Finite Group Databasebeta

#421×D167 #36332677

order21376
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#421×D167

Splittings

Fitting#421×C167 ⋊ C2
SylowC167 ⋊ C2×#421

Subgroups

subgroupG/H
centerC4C2×D4×D167
commutatorC4×C167C23×C4
FrattiniC2×C4C23×D167
Fitting#421×C167C2
socleC2×C167C22×C22⋊C4
prime radicalC2×#41×D167C2
cosocleC2×C4×C167C24
hypercenter#421D167
hypocenterC167C2×#421
LCSG ▷ C4×C167 ▷ C2×C167 ▷ C167
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2672

Conjugacy classes & character table

1870 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 13049);