Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C23×C4 |
| direct product | C31×#2642 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C31 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
416 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 3968 |
A minimal faithful permutation representation — 4 generators on 59 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)(32,33,34,35)(38,42)(40,43)(45,49)(50,52)(51,57)(58,59);(32,33,34,35)(36,37,39,41)(38,40,42,43)(44,45)(46,52)(47,51)(48,49)(50,54)(53,59)(55,58)(56,57);(32,33)(34,35)(36,38)(37,40)(39,42)(41,43)(44,46,48,54)(45,50,49,52)(47,55,56,53)(51,59,57,58);(44,47,48,56)(45,51,49,57)(46,53,54,55)(50,58,52,59)992 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#10095, C31×#10103, C31×#18441, … |
| maximal normal subgroup of | C31×#10095, C31×#10103, C31×#18441, … |
| maximal quotient of | C31×#14261, C31×#14274, C31×#14283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1374);