Finite Group Databasebeta

#537×C281 #31823132

order17984
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C24×C281 · Schur multiplier (H2) = C25

Aliases

direct product#537×C281

Subgroups

subgroupG/H
center, socleC22×C281C24
commutator, Frattini, cosocleC22C24×C281
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C281 ◁ G

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8992

Conjugacy classes & character table

6182 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#49094238, #49094272, #49094306, …
maximal subgroup of#1598×C281, #1604×C281, #1610×C281, …
maximal normal subgroup of#1598×C281, #1604×C281, #1610×C281, …
maximal quotient of#2311×C281, #2316×C281, #2323×C281, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17984, 218);