Finite Group Databasebeta

#534×C281 #31823129

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

Aliases

direct product#534×C281

Subgroups

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

346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4496

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#49094221, #49094255, #49094289, …
maximal subgroup of#1595×C281, #1601×C281, #1607×C281, …
maximal normal subgroup of#1595×C281, #1601×C281, #1607×C281, …
maximal quotient of#2308×C281, #2315×C281, #2321×C281, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17984, 215);