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C31×#2676 #16842609

order3968
nilpotency class2
isoclinismisoclinic class of #2668
automorphism?
homologyAbelianization (H1) = C24×C31 · Schur multiplier (H2) = C24×C4

Aliases

direct productC31×#2676

Subgroups

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

676 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)(33,35)(40,41,43,44)(42,45,46,47);(37,39)(41,44)(42,46);(32,33)(34,35)(36,37)(38,39)(40,41)(42,45)(43,44)(46,47);(32,33)(34,35)(40,42,43,46)(41,45,44,47)

Conjugacy classes & character table

992 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC31×#36706, C31×#36707, C31×#36712, …
maximal normal subgroup ofC31×#36706, C31×#36707, C31×#36712, …
maximal quotient ofC31×#14361, C31×#14362, C31×#14377, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3968, 1408);