Finite Group Databasebeta

#125×C433 #28357106

order13856
nilpotency class2
isoclinismisoclinic class of #120
automorphism?
homologyAbelianization (H1) = C23×C433 · Schur multiplier (H2) = C2

Aliases

direct product#125×C433

Subgroups

subgroupG/H
center, socle, prime radicalC22×C433C23
commutator, Frattini, cosocleC22C23×C433
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C433 ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13856

Conjugacy classes & character table

6062 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#42121553, #42122108, #42122115, …
maximal subgroup of#330×C433, #478×C433, #479×C433, …
maximal normal subgroup of#330×C433, #478×C433, #479×C433, …
maximal quotient of#382×C433, #387×C433, #389×C433, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13856, 32);