Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2403 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C22×C4 |
| direct product | C31×#2607 |
| 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 200 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 200 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)(40,41)(42,46)(43,44)(45,47)(48,49,52,51)(50,54,55,53);(33,36)(37,39)(41,44)(45,46)(50,55)(53,54);(32,33)(34,37)(35,36)(38,39)(40,41)(42,45)(43,44)(46,47)(48,50,52,55)(49,53,51,54);(32,34,35,38)(33,37,36,39)(40,42)(41,45)(43,47)(44,46)(48,51,52,49)(50,54,55,53)1178 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C31×#10386, C31×#10387, C31×#12121, … |
| maximal normal subgroup of | C31×#10386, C31×#10387, C31×#12121, … |
| maximal quotient of | C31×#13953, C31×#14091, C31×#14093, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1339);