Finite Group Databasebeta

C22×#16837168 #28586116

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C28

Aliases

direct productC22×#16837168

Splittings

SylowC59 ⋊ C22×#342

Subgroups

subgroupG/H
centerC24(C2×D59)⋊C4
commutatorC22×C59C22×C42
FrattiniC24C23×D59
FittingC23×C22⋊C4×C59C2
socleC24×C59C22⋊C4
prime radicalC26×C59C22
cosocleC24×C59C24
hypercenterC23×C22⋊C4D59
hypocenterC59C22×#342
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C26 ◁ C23×C22⋊C4

4334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 166995);