Finite Group Databasebeta

#546×C269 #31770283

order17216
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C269 · Schur multiplier (H2) = C25

Aliases

direct product#546×C269

Subgroups

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

334 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4304

Conjugacy classes & character table

6725 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#46822366, #46822391, #46822406, …
maximal subgroup of#3264×C269, #3266×C269, #3267×C269, …
maximal normal subgroup of#3264×C269, #3266×C269, #3267×C269, …
maximal quotient ofD4×C22⋊C4×C269, #2339×C269, #2342×C269, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17216, 227);