Finite Group Databasebeta

C22×#16838084 #29495678

order15104
automorphism?
homologyAbelianization (H1) = C26 · Schur multiplier (H2) = C213

Aliases

direct productC22×#16838084

Splittings

FittingC22×#125×C59 ⋊ C2
SylowC59 ⋊ C22×#552

Subgroups

subgroupG/H
centerC24C23×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC22×#125×C59C2
socleC24×C59C24
prime radicalC23×D236C22
hypercenterC22×#125D59
hypocenterC59C22×#552
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×#125

7934 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1724 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076557);