Finite Group Databasebeta

#546×C293 #34035807

order18752
nilpotency class2
automorphism?
homologyAbelianization (H1) = C24×C293 · Schur multiplier (H2) = C25

Aliases

direct product#546×C293

Subgroups

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

334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4688

Conjugacy classes & character table

7325 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49170266, #49170291, #49170306, …
maximal subgroup of#3264×C293, #3266×C293, #3267×C293, …
maximal normal subgroup of#3264×C293, #3266×C293, #3267×C293, …
maximal quotient ofD4×C22⋊C4×C293, #2339×C293, #2342×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 227);