Finite Group DatabasebetaFinite Group Databasebeta| order | 1984 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C31 · Schur multiplier (H2) = C2×C4 |
| direct product | C31×#495 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C31 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C31 |
| prime radical | C2×D8×C31 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C31 ◁ C42×C31 ◁ G | |
130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 992 |
A minimal faithful permutation representation — 3 generators on 51 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)(36,37)(38,44)(39,47)(40,42)(41,45)(43,48)(46,50)(49,51);(36,38,39,45,40,46,48,51)(37,41,43,44,42,49,47,50);(32,33,34,35)(37,42)(41,49)(43,47)(44,50)682 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1984, 176);