Finite Group Databasebeta

C2×#24923397 #36333063

order21376
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#24923397

Splittings

SylowC167 ⋊ C2×#446

Subgroups

subgroupG/H
centerC22×C4C22×D167
commutatorC22×C167C23×C4
FrattiniC2×C4C23×D167
FittingC2×#97×C167C2
socle, prime radicalC23×C167C22×C4
cosocleC2×C4×C167C24
hypercenterC2×#97D167
hypocenterC167C2×#446
LCSG ▷ C22×C167 ▷ C167
UCSC1 ◁ C22×C4 ◁ C2×#97

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 21376

Conjugacy classes & character table

3376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 13435);