Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C72 · Schur multiplier (H2) = C7 |
| direct product | C5×C72×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C2×C5×C72 | C22 |
| commutator, Frattini, cosocle | C2 | C22×C5×C72 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C5×C72 ◁ G | |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 1960 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3,4,5)(6,7,8,9,10,11,12)(20,21,22,23)(24,27,26,25);(13,14,15,16,17,18,19)(20,24,22,26)(21,25,23,27)1225 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 111);