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C2×C11×C19×C31 #27188366

order12958
nilpotency class1
isoclinismisoclinic class of C1
automorphism?
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC12958
abelianC2×C11×C19×C31
multiplicative(ℤ/12959)ˣ, (ℤ/25918)ˣ

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 63
transitive degreeμt(G) = 12958

A minimal faithful permutation representation — 1 generator on 63 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63)

Conjugacy classes & character table

12958 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic12958, D25916
Fitting subgroup ofC11×C19×Dic31, C11×C31×Dic19, C11×Dic589, …
socle ofC4×C11×C19×C31, C11×C19×Dic31, C11×C31×Dic19, …
maximal subgroup ofC4×C11×C19×C31, C11×C19×Dic31, C11×C31×Dic19, …
maximal normal subgroup ofC4×C11×C19×C31, C11×C19×Dic31, C11×C31×Dic19, …
maximal quotient ofC4×C11×C19×C31, C22×C11×C19×C31
automorphism group ofC12959
outer automorphism group ofC12959

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12958, 1);