Finite Group Databasebeta

#553×C251 #30631372

order16064
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C251 · Schur multiplier (H2) = C24

Aliases

direct product#553×C251

Subgroups

subgroupG/H
center, socleC22×C251C24
commutator, Frattini, cosocleC22C24×C251
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C251 ◁ G

238 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8032

Conjugacy classes & character table

6275 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44562209, #44562261, #44562335, …
maximal subgroup of#3297×C251, #3301×C251, #3307×C251, …
maximal normal subgroup of#3297×C251, #3301×C251, #3307×C251, …
maximal quotient of#2345×C251, #2347×C251, #2352×C251, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16064, 234);