Finite Group Databasebeta

C22×(C2×D419)⋊C4 #41000808

order26816
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×(C2×D419)⋊C4

Splittings

FittingC23×C4×C419 ⋊ C2
SylowC419 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC24C2×D419
commutatorC2×C419C23×C4
FrattiniC22C23×D419
FittingC23×C4×C419C2
socleC24×C419C22
prime radicalC24×D419C2
cosocleC22×C419C24
hypercenterC23×C4D419
hypocenterC419C22×C22⋊C4
LCSG ▷ C2×C419 ▷ C419
UCSC1 ◁ C24 ◁ C23×C4

674 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13408

Conjugacy classes & character table

6728 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26816, 996);