Finite Group Databasebeta

C22×#16837298 #28747034

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#16837298

Splittings

SylowC59 ⋊ C22×#389

Subgroups

subgroupG/H
centerC25C22×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
FittingC23×C4⋊C4×C59C2
socle, prime radicalC25×C59C23
cosocleC23×C59C25
hypercenterC23×C4⋊C4D59
hypocenterC59C22×#389
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C25 ◁ C23×C4⋊C4

4894 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15104

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, 327913);