Finite Group Databasebeta

#125×C449 #28385226

order14368
nilpotency class2
isoclinismisoclinic class of #120
automorphism?
homologyAbelianization (H1) = C23×C449 · Schur multiplier (H2) = C2

Aliases

direct product#125×C449

Subgroups

subgroupG/H
center, socle, prime radicalC22×C449C23
commutator, Frattini, cosocleC22C23×C449
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C449 ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14368

Conjugacy classes & character table

6286 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#43271749, #43272304, #43272311, …
maximal subgroup of#330×C449, #478×C449, #479×C449, …
maximal normal subgroup of#330×C449, #478×C449, #479×C449, …
maximal quotient of#382×C449, #387×C449, #389×C449, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14368, 32);