Finite Group Databasebeta

#121×C479 #29506264

order15328
nilpotency class2
isoclinismisoclinic class of #120
automorphism?
homologyAbelianization (H1) = C23×C479 · Schur multiplier (H2) = C23

Aliases

direct product#121×C479

Subgroups

subgroupG/H
center, socleC22×C479C23
commutator, Frattini, cosocleC22C23×C479
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C479 ◁ G

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7664

Conjugacy classes & character table

6706 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44500129, #44500528, #44500533, …
maximal subgroup of#327×C479, #447×C479, #448×C479, …
maximal normal subgroup of#327×C479, #447×C479, #448×C479, …
maximal quotient of#380×C479, #386×C479, #388×C479, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15328, 28);