Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C22 |
| direct product | C31×#2212 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | #459 |
| commutator, Frattini, cosocle | C2×C8 | C23×C31 |
| prime radical | C31×#509 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C2×C4×C31 ◁ C4×C8×C31 ◁ G | |
154 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 60 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)(34,42)(35,47)(36,51)(37,53)(38,43)(39,45)(40,44)(41,52)(46,60)(48,59)(49,63)(50,55)(54,56)(57,61)(58,62);(32,34,36,45,38,46,52,37)(33,39,41,42,43,53,51,60)(35,44,48,61,50,62,49,54)(40,55,56,59,58,47,57,63);(32,35)(33,40)(34,44)(36,48)(37,54)(38,50)(39,55)(41,56)(42,59)(43,58)(45,61)(46,62)(47,53)(49,52)(51,57)(60,63)713 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C31×#2212, C31×#33594, C31×#33595, … |
| maximal normal subgroup of | C2×C31×#2212, C31×#33594, C31×#33595, … |
| maximal quotient of | C31×#12416, C31×#12417, C31×#12420, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 944);