Finite Group Databasebeta

C22×#16837164 #28586084

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

Aliases

direct productC22×#16837164

Splittings

SylowC59 ⋊ C22×#340

Subgroups

subgroupG/H
centerC25C22⋊D59
commutatorC4×C59C22×C42
FrattiniC22×C4C23×D59
FittingC23×C4⋊C4×C59C2
socle, prime radicalC25×C59D4
cosocleC22×C4×C59C24
hypercenterC23×C4⋊C4D59
hypocenterC59C22×#340
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C25 ◁ C24×C4 ◁ C23×C4⋊C4

3006 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

Conjugacy classes & character table

2432 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 166963);