Finite Group Databasebeta

#560×C293 #34035821

order18752
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C293 · Schur multiplier (H2) = C24

Aliases

direct product#560×C293

Subgroups

subgroupG/H
center, socleC22×C293C24
commutator, Frattini, cosocleC22C24×C293
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C293 ◁ G

252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4688

Conjugacy classes & character table

5567 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49160792, #560×D293, #49172920, …
maximal subgroup of#2200×C293, C2×#560×C293, #3529×C293, …
maximal normal subgroup of#2200×C293, C2×#560×C293, #3529×C293, …
maximal quotient of#2375×C293, #2376×C293, #2377×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 241);