Finite Group Databasebeta

#543×C293 #34035804

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

Aliases

direct product#543×C293

Subgroups

subgroupG/H
center, socleC22×C293C24
commutator, Frattini, cosocleC22C24×C293
prime radicalC24×C293C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C293 ◁ G

242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4688

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#49157708, #49157742, #49157776, …
maximal subgroup of#1596×C293, #1602×C293, #1608×C293, …
maximal normal subgroup of#1596×C293, #1602×C293, #1608×C293, …
maximal quotient of#2315×C293, #2329×C293, #2437×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 224);