Finite Group Databasebeta

#562×C269 #31770299

order17216
nilpotency class2
isoclinismisoclinic class of #560
automorphism?
homologyAbelianization (H1) = C24×C269 · Schur multiplier (H2) = C24

Aliases

direct product#562×C269

Subgroups

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

220 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8608

Conjugacy classes & character table

5111 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#46810178, #46810202, #46810208, …
maximal subgroup of#1656×C269, #1661×C269, #1662×C269, …
maximal normal subgroup of#1656×C269, #1661×C269, #1662×C269, …
maximal quotient of#2376×C269, #2377×C269, #2378×C269, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17216, 243);