Finite Group Databasebeta

C22×#20269748 #41003287

order26944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×#20269748

Splittings

FittingC23×C4×C421 ⋊ C2
SylowC421 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D421
commutatorC2×C421C23×C4
FrattiniC22C23×D421
FittingC23×C4×C421C2
socleC24×C421C22
prime radicalC24×D421C2
cosocleC22×C421C24
hypercenterC23×C4D421
hypocenterC421C22×C22⋊C4
LCSG ▷ C2×C421 ▷ C421
UCSC1 ◁ C24 ◁ C23×C4

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13472

Conjugacy classes & character table

6760 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26944, 996);