Finite Group Databasebeta

#127×C419 #27211606

order13408
nilpotency class2
isoclinismisoclinic class of #120
automorphism?
homologyAbelianization (H1) = C23×C419 · Schur multiplier (H2) = C22×C4

Aliases

direct product#127×C419

Subgroups

subgroupG/H
center, socleC22×C419C23
commutator, Frattini, cosocleC22C23×C419
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C419 ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6704

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#41000105, #41000154, #41000528, …
maximal subgroup of#331×C419, #353×C419, #453×C419, …
maximal normal subgroup of#331×C419, #353×C419, #453×C419, …
maximal quotient of#384×C419, #390×C419, #392×C419, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13408, 34);