Finite Group Databasebeta

#540×C293 #34035801

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

Aliases

direct product#540×C293

Subgroups

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

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9376

Conjugacy classes & character table

6446 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49168978, #49169023, #49169071, …
maximal subgroup of#3119×C293, #3122×C293, #3126×C293, …
maximal normal subgroup of#3119×C293, #3122×C293, #3126×C293, …
maximal quotient of#2314×C293, #2319×C293, #2324×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 221);