Finite Group Databasebeta

#560×C283 #31826157

order18112
nilpotency class2
isoclinismisoclinic class of #560
automorphism?
homologyAbelianization (H1) = C24×C283 · Schur multiplier (H2) = C24

Aliases

direct product#560×C283

Subgroups

subgroupG/H
center, socleC22×C283C24
commutator, Frattini, cosocleC22C24×C283
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C283 ◁ G

252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4528

Conjugacy classes & character table

5377 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49123268, #560×D283, #49135396, …
maximal subgroup of#2200×C283, C2×#560×C283, #3529×C283, …
maximal normal subgroup of#2200×C283, C2×#560×C283, #3529×C283, …
maximal quotient of#2375×C283, #2376×C283, #2377×C283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18112, 241);