Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2202 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C23 |
| direct product | C31×#2203 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×Q8 | C23×C31 |
| prime radical | C31×#454 | C2 |
| LCS | G ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C22×C31 ◁ C2×Q8×C31 ◁ G | |
216 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 63 |
| transitive degree | μt(G) = 992 |
A minimal faithful permutation representation — 3 generators 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)(34,43)(35,47)(36,39)(37,42)(38,44)(40,50)(41,52)(45,60)(46,58)(48,56)(49,57)(51,61)(53,59)(54,62)(55,63);(32,34,37,46)(33,38,42,56)(35,48,50,44)(36,51,52,45)(39,54,41,55)(40,58,47,43)(49,62,53,63)(57,60,59,61);(33,39)(36,52)(38,54)(40,59)(41,42)(43,60)(45,51)(47,57)(49,53)(55,56)(58,61)(62,63)527 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#13679, C31×#13680, C2×C31×#2203, … |
| maximal normal subgroup of | C31×#13679, C31×#13680, C2×C31×#2203, … |
| maximal quotient of | C31×#12097, C31×#12098, C31×#12126, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 935);