Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C24 |
| direct product | C31×#2817 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C31 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| prime radical | C24×C31 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
444 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 184 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) = 1984 |
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)(37,40)(41,43)(44,45,49,47)(46,52,54,50)(48,51,57,55)(53,59,56,58);(33,35)(37,40)(38,42)(44,46,49,54)(45,50,47,52)(48,56,57,53)(51,59,55,58);(32,33)(34,35)(36,37)(38,41)(39,40)(42,43)(44,47,49,45)(46,50,54,52)(48,51,57,55)(53,59,56,58);(36,38)(37,41)(39,42)(40,43)(44,48,49,57)(45,51,47,55)(46,53,54,56)(50,58,52,59)806 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#9982, C31×#9985, C31×#12095, … |
| maximal normal subgroup of | C31×#9982, C31×#9985, C31×#12095, … |
| maximal quotient of | C31×#14626, C31×#14627, C31×#14629, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1549);