Finite Group Databasebeta

#550×C269 #31770287

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

Aliases

direct product#550×C269

Subgroups

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

312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8608

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#46809950, #46810012, #46810078, …
maximal subgroup of#1621×C269, #1631×C269, #1641×C269, …
maximal normal subgroup of#1621×C269, #1631×C269, #1641×C269, …
maximal quotient of#2341×C269, Q8×C4⋊C4×C269, #2354×C269, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17216, 231);