Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C23×C4 |
| direct product | C31×#2804 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C31 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| prime radical | C22×D4×C31 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
480 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1984 |
A minimal faithful permutation representation — 4 generators on 55 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)(33,36)(34,38)(40,41,43,44)(42,45,46,47)(48,49)(50,53)(51,52)(54,55);(33,36)(37,39)(41,44)(42,46)(49,51)(50,54);(32,33)(34,37)(35,36)(38,39)(40,41)(42,45)(43,44)(46,47)(48,50,52,54)(49,53,51,55);(32,34,35,38)(33,37,36,39)(40,42)(41,45)(43,46)(44,47)(48,51,52,49)(50,55,54,53)992 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#7745, C31×#7755, C31×#7782, … |
| maximal normal subgroup of | C31×#7745, C31×#7755, C31×#7782, … |
| maximal quotient of | C31×#14440, C31×#14457, C31×#14471, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1536);