Finite Group Databasebeta

C2×#24923826 #36337429

order21376
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#24923826

Splittings

SylowC167 ⋊ C2×#533

Subgroups

subgroupG/H
centerC22×C4C22×D167
commutator, cosocleC22×C167C25
FrattiniC22C24×D167
FittingC22×C42×C167C2
socleC23×C167C24
prime radicalC24×C167C23
hypercenterC22×C42D167
hypocenterC167C2×#533
LCSG ▷ C22×C167 ▷ C167
UCSC1 ◁ C22×C4 ◁ C22×C42

1168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10688

Conjugacy classes & character table

5368 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 17801);