Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2021 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C24 |
| direct product | C31×#2022 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | #120 |
| commutator, Frattini, cosocle | C24 | C23×C31 |
| prime radical | C31×#534 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C24×C31 ◁ G | |
430 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 992 |
A minimal faithful permutation representation — 3 generators on 51 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)(36,37)(38,41)(39,42)(40,43)(44,47)(45,48)(46,50)(49,51);(36,38,40,45)(37,41,43,48)(39,44,46,51)(42,49,50,47);(33,35)(36,39)(37,42)(38,44)(40,46)(41,47)(43,50)(45,51)(48,49)806 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#7395, C31×#12092, C31×#12094, … |
| maximal normal subgroup of | C31×#7395, C31×#12092, C31×#12094, … |
| maximal quotient of | C31×#9918, C31×#9919, C31×#9920, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 754);