Finite Group Databasebeta

C22×#20261943 #38734546

order24896
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×#20261943

Splittings

FittingC23×C4×C389 ⋊ C2
SylowC389 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D389
commutatorC2×C389C23×C4
FrattiniC22C23×D389
FittingC23×C4×C389C2
socleC24×C389C22
prime radicalC24×D389C2
cosocleC22×C389C24
hypercenterC23×C4D389
hypocenterC389C22×C22⋊C4
LCSG ▷ C2×C389 ▷ C389
UCSC1 ◁ C24 ◁ C23×C4

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12448

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, 996);