Finite Group Databasebeta

C22×#16838087 #29495675

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

Aliases

direct productC22×#16838087

Splittings

FittingC23×C4⋊C4×C59 ⋊ C2
SylowC59 ⋊ C22×#552

Subgroups

subgroupG/H
centerC24C23×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC23×C4⋊C4×C59C2
socleC24×C59C24
prime radicalC23×C22⋊D59C22
hypercenterC23×C4⋊C4D59
hypocenterC59C22×#552
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C24 ◁ C23×C4⋊C4

7934 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 1076554);