Finite Group Databasebeta

C2×#27159291 #38733943

order24896
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#27159291

Splittings

SylowC389 ⋊ C2×#95

Subgroups

subgroupG/H
centerC24C2×D389
commutatorC2×C389C2×C42
FrattiniC23C22×D389
FittingC23×C4×C389C2
socle, prime radicalC24×C389C22
cosocleC23×C389C23
hypercenterC23×C4D389
hypocenterC389C2×#95
LCSG ▷ C2×C389 ▷ C389
UCSC1 ◁ C24 ◁ C23×C4

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24896

Conjugacy classes & character table

6248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 393);