Finite Group Databasebeta

C22⋊C4×C22⋊Dic59 #28510091

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27×C4

Aliases

direct productC22⋊C4×C22⋊Dic59

Splittings

SylowC59 ⋊ C22⋊C42

Subgroups

subgroupG/H
center, FrattiniC24C23×D59
commutatorC22×C59C22×C42
FittingC23×C22⋊C4×C59C2
socle, cosocleC24×C59C24
prime radicalC26×C59C22
hypercenterC23×C22⋊C4D59
hypocenterC59C22⋊C42
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C23×C22⋊C4

4254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 90970);