Finite Group Databasebeta

C2×#24923864 #36337487

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

Aliases

direct productC2×#24923864

Splittings

SylowC167 ⋊ C2×#539

Subgroups

subgroupG/H
centerC23C23×D167
commutator, cosocleC22×C167C25
FrattiniC22C24×D167
Fitting, prime radicalC2×#121×C167C2
socleC23×C167C24
hypercenterC2×#121D167
hypocenterC167C2×#539
LCSG ▷ C22×C167 ▷ C167
UCSC1 ◁ C23 ◁ C2×#121

1144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10688

Conjugacy classes & character table

2368 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 17859);