Finite Group Databasebeta

C2×#27159371 #38734615

order24896
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#27159371

Splittings

SylowC389 ⋊ C2×#124

Subgroups

subgroupG/H
centerC23C22×D389
commutator, cosocleC22×C389C24
FrattiniC22C23×D389
Fitting, prime radicalC22×D4×C389C2
socleC23×C389C23
hypercenterC22×D4D389
hypocenterC389C2×#124
LCSG ▷ C22×C389 ▷ C389
UCSC1 ◁ C23 ◁ C22×D4

330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12448

Conjugacy classes & character table

3908 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24896, 1065);