Finite Group Databasebeta

C22⋊C4×D673 #36340427

order21536
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC22⋊C4×D673

Splittings

FittingC22⋊C4×C673 ⋊ C2
SylowC673 ⋊ C2×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C22×D673
commutatorC2×C673C22×C4
FittingC22⋊C4×C673C2
socle, cosocleC22×C673C23
prime radicalC23×D673C2
hypercenterC22⋊C4D673
hypocenterC673C2×C22⋊C4
LCSG ▷ C2×C673 ▷ C673
UCSC1 ◁ C22 ◁ C22⋊C4

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5384

Conjugacy classes & character table

3380 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21536, 96);