Finite Group Databasebeta

C22×#16837320 #28754876

order15104
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productC22×#16837320

Splittings

FittingC22×#95×C59 ⋊ C2
SylowC59 ⋊ C22×#394

Subgroups

subgroupG/H
centerC25C22×D59
commutator, cosocleC23×C59C25
FrattiniC23C24×D59
FittingC22×#95×C59C2
socleC25×C59C23
prime radicalC24×D236C2
hypercenterC22×#95D59
hypocenterC59C22×#394
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C25 ◁ C22×#95

8798 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 335755);