Finite Group Databasebeta

C2×#24923197 #36327365

order21376
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#24923197

Splittings

SylowC167 ⋊ C2×#397

Subgroups

subgroupG/H
centerC24C22×D167
commutator, cosocleC23×C167C24
FrattiniC23C23×D167
FittingC22×C22⋊C4×C167C2
socleC24×C167C23
prime radicalC25×C167C22
hypercenterC22×C22⋊C4D167
hypocenterC167C2×#397
LCSG ▷ C23×C167 ▷ C167
UCSC1 ◁ C24 ◁ C22×C22⋊C4

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10688

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, 7737);