Finite Group Databasebeta

C22⋊C4×C22⋊Dic73 #33007386

order18688
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27×C4

Aliases

direct productC22⋊C4×C22⋊Dic73

Splittings

SylowC73 ⋊ C22⋊C42

Subgroups

subgroupG/H
center, FrattiniC24C23×D73
commutatorC22×C73C22×C42
FittingC23×C22⋊C4×C73C2
socle, cosocleC24×C73C24
prime radicalC26×C73C22
hypercenterC23×C22⋊C4D73
hypocenterC73C22⋊C42
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C23×C22⋊C4

4254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

2980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 90970);