Finite Group Databasebeta

C22×#16837186 #28741386

order15104
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#16837186

Splittings

SylowC59 ⋊ C22×#350

Subgroups

subgroupG/H
centerC22×C8C22⋊D59
commutatorC4×C59C23×C8
FrattiniC2×C8C23×D59
FittingC22×#131×C59C2
socleC23×C59C22⋊C8
prime radicalC22×#41×C59C4
cosocleC2×C8×C59C24
hypercenterC22×#131D59
hypocenterC59C22×#350
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C22×#131

1174 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

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, 322265);