Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C22 |
| direct product | C31×#2209 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C31 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C31 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C42×C31 ◁ C4×C8×C31 ◁ G | |
154 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 3968 |
A minimal faithful permutation representation — 3 generators on 67 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)(36,37,41,45)(38,46,49,65)(39,50,54,64)(40,55,52,44)(42,57,59,47)(43,60,62,53)(48,66,56,61)(51,63,67,58);(32,33,34,35);(36,38,41,49)(37,42,45,59)(39,51,54,67)(40,56,52,48)(43,61,62,66)(44,63,55,58)(46,64,65,50)(47,60,57,53)899 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#12321, C31×#12322, C31×#12327, … |
| maximal normal subgroup of | C31×#12321, C31×#12322, C31×#12327, … |
| maximal quotient of | C31×#12421, C31×#12427, C31×#12448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 941);