Finite Group Databasebeta

C22×#20264343 #38786561

order25664
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×#20264343

Splittings

FittingC23×C4×C401 ⋊ C2
SylowC401 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D401
commutatorC2×C401C23×C4
FrattiniC22C23×D401
FittingC23×C4×C401C2
socleC24×C401C22
prime radicalC24×D401C2
cosocleC22×C401C24
hypercenterC23×C4D401
hypocenterC401C22×C22⋊C4
LCSG ▷ C2×C401 ▷ C401
UCSC1 ◁ C24 ◁ C23×C4

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12832

Conjugacy classes & character table

6440 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25664, 996);