Finite Group Databasebeta

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C31×#2657 #16842590

order3968
nilpotency class2
isoclinismisoclinic class of #2613
automorphism?
homologyAbelianization (H1) = C24×C31 · Schur multiplier (H2) = C22×C43

Aliases

direct productC31×#2657

Subgroups

subgroupG/H
center, socleC23×C31C24
commutator, Frattini, cosocleC23C24×C31
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C31 ◁ G

844 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 1984

A minimal faithful permutation representation — 4 generators on 47 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)(40,41)(42,44)(43,45)(46,47);(36,37,38,39)(40,41,43,45)(42,44,47,46);(32,33)(34,35)(36,37)(38,39)(40,41)(42,46)(43,45)(44,47);(40,42,43,47)(41,44,45,46)

Conjugacy classes & character table

992 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC31×#10088, C31×#10096, C31×#18426, …
maximal normal subgroup ofC31×#10088, C31×#10096, C31×#18426, …
maximal quotient ofC31×#14272, C31×#14273, C31×#14321, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1389);