Finite Group Databasebeta

#555×C269 #31770292

order17216
nilpotency class2
isoclinismisoclinic class of D42
automorphism?
homologyAbelianization (H1) = C24×C269 · Schur multiplier (H2) = C23×C4

Aliases

direct product#555×C269

Subgroups

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

236 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#46809968, #46810030, #46810113, …
maximal subgroup of#1624×C269, #1634×C269, #1646×C269, …
maximal normal subgroup of#1624×C269, #1634×C269, #1646×C269, …
maximal quotient of#2346×C269, #2354×C269, #2363×C269, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17216, 236);