Finite Group Databasebeta

C22×#16837179 #28741342

order15104
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25

Aliases

direct productC22×#16837179

Splittings

SylowC59 ⋊ C22×#347

Subgroups

subgroupG/H
centerC22×C4C4×Dic59
commutatorC4×C59C22×C42
FrattiniC2×C8C23×D59
FittingC22×M32×C59C2
socleC23×C59#97
prime radicalC24×C59M16
cosocleC2×C8×C59C24
hypercenterC22×M32D59
hypocenterC59C22×#347
LCSG ▷ C4×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C22×M32

782 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, 322221);