Finite Group Databasebeta

#399×C293 #34035660

order18752
nilpotency class2
automorphism?
homologyAbelianization (H1) = C23×C293 · Schur multiplier (H2) = C23

Aliases

direct product#399×C293

Subgroups

subgroupG/H
center, socleC23×C293C23
commutator, Frattini, cosocleC23C23×C293
prime radicalC24×C293C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C293 ◁ G

186 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#49156809, #49157804, #49157809, …
maximal subgroup of#1352×C293, #1613×C293, #1614×C293, …
maximal normal subgroup of#1352×C293, #1613×C293, #1614×C293, …
maximal quotient of#1439×C293, #1444×C293, #1445×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 80);