Finite Group Databasebeta

C2×#24923040 #36323880

order21376
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#24923040

Splittings

SylowC167 ⋊ C2×#344

Subgroups

subgroupG/H
centerC2×C4C22⋊Dic167
commutatorC22×C167C2×C42
FrattiniC22×C4C22×D167
FittingC22×M16×C167C2
socleC22×C167#95
prime radicalC24×C167C2×C4
cosocleC22×C4×C167C23
hypercenterC22×M16D167
hypocenterC167C2×#344
LCSG ▷ C22×C167 ▷ C2×C167 ▷ C167
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5344

Conjugacy classes & character table

3364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 4252);