Finite Group Databasebeta

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#560×C251 #30631379

order16064
nilpotency class2
isoclinismisoclinic class of #560
automorphism?
homologyAbelianization (H1) = C24×C251 · Schur multiplier (H2) = C24

Aliases

direct product#560×C251

Subgroups

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

252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4016

Conjugacy classes & character table

4769 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44552372, #560×D251, #44564500, …
maximal subgroup of#2200×C251, C2×#560×C251, #3529×C251, …
maximal normal subgroup of#2200×C251, C2×#560×C251, #3529×C251, …
maximal quotient of#2375×C251, #2376×C251, #2377×C251, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16064, 241);