Finite Group DatabasebetaFinite Group Databasebeta| order | 1936 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C112 · Schur multiplier (H2) = C2×C11 |
| direct product | C112×C4⋊C4 |
| unambiguous semidirect product | C4⋊(C4×C112) |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C112 | C22 |
| commutator | C2 | C2×C4×C112 |
| Frattini, cosocle | C22 | C22×C112 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C112 ◁ G | |
182 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 1936 |
A minimal faithful permutation representation — 2 generators on 30 points:
(1,2,3,4,5,6,7,8,9,10,11)(24,26)(27,28,29,30);(12,13,14,15,16,17,18,19,20,21,22)(23,24,25,26)1210 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1936, 97);