Finite Group Databasebeta

#121×C449 #28385222

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

Aliases

direct product#121×C449

Subgroups

subgroupG/H
center, socleC22×C449C23
commutator, Frattini, cosocleC22C23×C449
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C449 ◁ G

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7184

Conjugacy classes & character table

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

Relationships

Fitting subgroup of#43271741, #43272140, #43272145, …
maximal subgroup of#327×C449, #447×C449, #448×C449, …
maximal normal subgroup of#327×C449, #447×C449, #448×C449, …
maximal quotient of#380×C449, #386×C449, #388×C449, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14368, 28);