Finite Group Databasebeta

C22×#16838076 #29495667

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

Aliases

direct productC22×#16838076

Splittings

FittingC22×#117×C59 ⋊ C2
SylowC59 ⋊ C22×#551

Subgroups

subgroupG/H
centerC24C23×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC22×#117×C59C2
socleC24×C59C24
prime radicalC22×#14273697C2
hypercenterC22×#117D59
hypocenterC59C22×#551
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C22×#117

9526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

2420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 1076546);