Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C24 |
| direct product | C31×#2644 |
| 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 | |
420 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 420 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) = 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)(37,38)(40,41)(42,45)(43,46)(44,47)(48,49,52,54)(50,55,51,53);(32,33,35,36)(34,37,39,38)(40,42)(41,43)(44,46)(45,47)(48,50,52,51)(49,53,54,55);(32,33)(34,38)(35,36)(37,39)(40,42)(41,45)(43,47)(44,46)(48,49)(50,53)(51,55)(52,54);(32,34,35,39)(33,37,36,38)(40,43,44,45)(41,46,47,42)(48,51,52,50)(49,53,54,55)992 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#29436, C31×#29437, C31×#29442, … |
| maximal normal subgroup of | C31×#29436, C31×#29437, C31×#29442, … |
| maximal quotient of | C31×#14260, C31×#14266, C31×#14331, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1376);