Finite Group Databasebeta

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#127×C499 #30630239

order15968
nilpotency class2
isoclinismisoclinic class of #120
automorphism?
homologyAbelianization (H1) = C23×C499 · Schur multiplier (H2) = C22×C4

Aliases

direct product#127×C499

Subgroups

subgroupG/H
center, socleC22×C499C23
commutator, Frattini, cosocleC22C23×C499
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C499 ◁ G

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7984

Conjugacy classes & character table

6986 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of#44542842, #44542891, #44543265, …
maximal subgroup of#331×C499, #353×C499, #453×C499, …
maximal normal subgroup of#331×C499, #353×C499, #453×C499, …
maximal quotient of#384×C499, #390×C499, #392×C499, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15968, 34);