Finite Group Databasebeta

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#560×C271 #31773589

order17344
nilpotency class2
isoclinismisoclinic class of #560
automorphism?
homologyAbelianization (H1) = C24×C271 · Schur multiplier (H2) = C24

Aliases

direct product#560×C271

Subgroups

subgroupG/H
center, socleC22×C271C24
commutator, Frattini, cosocleC22C24×C271
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C271 ◁ G

252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4336

Conjugacy classes & character table

5149 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#46838371, #560×D271, #46850499, …
maximal subgroup of#2200×C271, C2×#560×C271, #3529×C271, …
maximal normal subgroup of#2200×C271, C2×#560×C271, #3529×C271, …
maximal quotient of#2375×C271, #2376×C271, #2377×C271, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17344, 241);