Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C23 |
| direct product | C31×#2843 |
| 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 | |
348 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 348 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) = 3968 |
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)(32,33,35,37)(34,36,38,39)(40,41)(42,46)(43,47)(44,45);(34,38)(36,39)(41,45)(43,46)(48,49,51,53)(50,54,55,52);(32,33)(34,36)(35,37)(38,39)(40,42)(41,46)(43,45)(44,47)(48,50,51,55)(49,52,53,54);(32,34)(33,36)(35,38)(37,39)(40,43,44,46)(41,47,45,42)806 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#12183, C31×#12259, C2×C31×#2843, … |
| maximal normal subgroup of | C31×#12183, C31×#12259, C2×C31×#2843, … |
| maximal quotient of | C31×#14638, C31×#14639, C31×#14640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1575);