Finite Group Databasebeta

#398×C293 #34035659

order18752
nilpotency class2
automorphism?
homologyAbelianization (H1) = C23×C293 · Schur multiplier (H2) = C22

Aliases

direct product#398×C293

Subgroups

subgroupG/H
center, socle, prime radicalC23×C293C23
commutator, Frattini, cosocleC23C23×C293
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C293 ◁ G

150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18752

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#49156791, #49157780, #49157787, …
maximal subgroup of#1346×C293, #1609×C293, #1610×C293, …
maximal normal subgroup of#1346×C293, #1609×C293, #1610×C293, …
maximal quotient of#1441×C293, #1442×C293, #1444×C293, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18752, 79);