Finite Group Databasebeta

C22×#16837174 #28586143

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

Aliases

direct productC22×#16837174

Splittings

SylowC59 ⋊ C22×#344

Subgroups

subgroupG/H
centerC22×C4(C2×D59)⋊C4
commutatorC22×C59C22×C42
FrattiniC22×C4C23×D59
FittingC23×M16×C59C2
socleC23×C59#95
prime radicalC25×C59C2×C4
cosocleC22×C4×C59C24
hypercenterC23×M16D59
hypocenterC59C22×#344
LCSG ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C24×C4 ◁ C23×M16

2190 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, 167022);