Finite Group Databasebeta

#440×D167 #36332913

order21376
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#440×D167

Splittings

Fitting#440×C167 ⋊ C2
SylowC167 ⋊ C2×#440

Subgroups

subgroupG/H
centerC22C2×D4×D167
commutatorC4×C167C23×C4
FrattiniC2×C4C23×D167
Fitting#440×C167C2
socleC22×C167C22×D4
prime radicalC2×D4×D167C22
cosocleC2×C4×C167C24
hypercenter#440D167
hypocenterC167C2×#440
LCSG ▷ C4×C167 ▷ C2×C167 ▷ C167
UCSC1 ◁ C22 ◁ C42 ◁ #440

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5344

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, 13285);