Finite Group DatabasebetaFinite Group Databasebeta| order | 3968 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C31 · Schur multiplier (H2) = C25 |
| direct product | C31×#2760 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C31 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C31 |
| prime radical | C31×#392 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C31 ◁ G | |
520 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 176 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)(40,41,44,42)(43,46,47,45)(48,49)(50,54)(51,52)(53,55);(33,36)(37,39)(41,42)(43,47)(49,52)(50,55);(32,33,35,36)(34,37,38,39)(40,42,44,41)(43,46,47,45)(48,50)(49,53)(51,55)(52,54);(32,34)(33,37)(35,38)(36,39)(40,43)(41,45)(42,46)(44,47)(48,49)(50,53)(51,52)(54,55)992 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#12187, C31×#12263, C31×#36776, … |
| maximal normal subgroup of | C31×#12187, C31×#12263, C31×#36776, … |
| maximal quotient of | C31×#14375, C31×#14508, C31×#14572, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3968, 1492);