Finite Group DatabasebetaFinite Group Databasebeta| order | 903 |
| isoclinism | isoclinic class of #11744749 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C43 ⋊ C3 |
| Sylow | C43 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C43 | C3 |
| LCS | G ▷ C7×C43 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 50 |
| transitive degree | μt(G) = 301 |
Polycyclic presentation:
3,7,43|b^a=b^4,c^a=c^6103 conjugacy classes — view the full character table.
| maximal subgroup of | #14268588, #14268592, #14268594, … |
| maximal normal subgroup of | #14268588, #14268592, #14268594, … |
| maximal quotient of | C2×#11744749, #14582151, C3×#11744749, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(903, 6);