Finite Group Databasebeta

#537×C269 #31770274

order17216
nilpotency class2
isoclinismisoclinic class of #534
automorphism?
homologyAbelianization (H1) = C24×C269 · Schur multiplier (H2) = C25

Aliases

direct product#537×C269

Subgroups

subgroupG/H
center, socleC22×C269C24
commutator, Frattini, cosocleC22C24×C269
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C269 ◁ G

294 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8608

Conjugacy classes & character table

5918 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#46809820, #46809854, #46809888, …
maximal subgroup of#1598×C269, #1604×C269, #1610×C269, …
maximal normal subgroup of#1598×C269, #1604×C269, #1610×C269, …
maximal quotient of#2311×C269, #2316×C269, #2323×C269, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17216, 218);