Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C31 · Schur multiplier (H2) = C27×C4 |
| direct product | C31×#3549 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C31 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ G | |
1258 conjugacy classes of subgroups; only the 768 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 768 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 992 |
A minimal faithful permutation representation — 5 generators on 47 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)(33,35)(37,38)(41,44)(42,43);(32,33,36,35)(34,38,39,37)(40,41,45,44)(42,47,43,46);(40,42,45,43)(41,46,44,47);(32,34,36,39)(33,37,35,38)(40,43,45,42)(41,47,44,46);(32,35,36,33)(34,38,39,37)(40,44,45,41)(42,47,43,46)1178 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C31×#8491, C31×#8530, C31×#12769, … |
| maximal normal subgroup of | C31×#8491, C31×#8530, C31×#12769, … |
| maximal quotient of | C31×#34368, C31×#34415, C31×#34485, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 2281);