Finite Group Databasebeta

C22×#16837282 #28747003

order15104
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C212

Aliases

direct productC22×#16837282

Splittings

SylowC59 ⋊ C22×#386

Subgroups

subgroupG/H
centerC25C22×D59
commutatorC22×C59C24×C4
FrattiniC23C24×D59
Fitting, prime radicalC24×D4×C59C2
socleC25×C59C23
cosocleC23×C59C25
hypercenterC24×D4D59
hypocenterC59C22×#386
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C25 ◁ C24×D4

11630 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, 327882);