Finite Group Databasebeta

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#542×C269 #31770279

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

Aliases

direct product#542×C269

Subgroups

subgroupG/H
center, socleC22×C269C24
commutator, Frattini, cosocleC22C24×C269
prime radical#121×C269C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C269 ◁ G

216 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#46821063, #46821108, #46821141, …
maximal subgroup of#3118×C269, #3121×C269, #3124×C269, …
maximal normal subgroup of#3118×C269, #3121×C269, #3124×C269, …
maximal quotient of#2314×C269, #2319×C269, #2320×C269, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17216, 223);