Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C24×C4 |
| direct product | C31×#2501 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C31 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| prime radical | C2×C31×#121 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
708 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(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)(33,34)(37,38)(40,41,44,46)(42,43,45,47);(32,33,35,34)(36,37,39,38)(40,42)(41,43)(44,45)(46,47);(36,37,39,38)(40,43)(41,45)(42,46)(44,47);(32,34,35,33)(36,38,39,37)1178 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C31×#9464, C31×#9952, C31×#9960, … |
| maximal normal subgroup of | C31×#9464, C31×#9952, C31×#9960, … |
| maximal quotient of | C31×#13880, C31×#13904, C31×#13996, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1233);