Finite Group DatabasebetaFinite Group Databasebeta| order | 1400 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 483840 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23×C5 |
| abelian | C23×C52×C7 |
| multiplicative | (ℤ/2343)ˣ, (ℤ/3124)ˣ, (ℤ/4686)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
256 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 1400 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2)(7,8,9,10,11)(17,18,19,20,21,22,23);(3,4)(12,13,14,15,16);(5,6)1400 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1400, 153);