Finite Group Databasebeta

#121×C491 #30628219

order15712
nilpotency class2
isoclinismisoclinic class of #120
automorphism?
homologyAbelianization (H1) = C23×C491 · Schur multiplier (H2) = C23

Aliases

direct product#121×C491

Subgroups

subgroupG/H
center, socleC22×C491C23
commutator, Frattini, cosocleC22C23×C491
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C491 ◁ G

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7856

Conjugacy classes & character table

6874 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44536459, #44536858, #44536863, …
maximal subgroup of#327×C491, #447×C491, #448×C491, …
maximal normal subgroup of#327×C491, #447×C491, #448×C491, …
maximal quotient of#380×C491, #386×C491, #388×C491, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15712, 28);