Finite Group Databasebeta

C2×#104×D167 #36332673

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

Aliases

direct productC2×#104×D167

Splittings

FittingC2×#104×C167 ⋊ C2
SylowC167 ⋊ C22×#104

Subgroups

subgroupG/H
centerC2×C4D4×D167
commutatorC4×C167C23×C4
FrattiniC2×C4C23×D167
FittingC2×#104×C167C2
socleC22×C167C2×C22⋊C4
prime radicalC2×#41×D167C2
cosocleC2×C4×C167C24
hypercenterC2×#104D167
hypocenterC167C22×#104
LCSG ▷ C4×C167 ▷ C2×C167 ▷ C167
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

856 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2672

Conjugacy classes & character table

2380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 13045);