Finite Group Databasebeta

#125×C419 #27211604

order13408
nilpotency class2
isoclinismisoclinic class of #120
automorphism?
homologyAbelianization (H1) = C23×C419 · Schur multiplier (H2) = C2

Aliases

direct product#125×C419

Subgroups

subgroupG/H
center, socle, prime radicalC22×C419C23
commutator, Frattini, cosocleC22C23×C419
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C419 ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13408

Conjugacy classes & character table

5866 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#41000103, #41000658, #41000665, …
maximal subgroup of#330×C419, #478×C419, #479×C419, …
maximal normal subgroup of#330×C419, #478×C419, #479×C419, …
maximal quotient of#382×C419, #387×C419, #389×C419, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13408, 32);