Finite Group Databasebeta

#541×C293 #34035802

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

Aliases

direct product#541×C293

Subgroups

subgroupG/H
center, socleC22×C293C24
commutator, Frattini, cosocleC22C24×C293
prime radicalC23×C293C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C293 ◁ G

192 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#49168993, #49169032, #49169080, …
maximal subgroup of#3120×C293, #3123×C293, #3127×C293, …
maximal normal subgroup of#3120×C293, #3123×C293, #3127×C293, …
maximal quotient of#2314×C293, #2320×C293, #2323×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 222);