Finite Group DatabasebetaFinite Group Databasebeta| order | 4284 |
| isoclinism | isoclinic class of C7⋊#157 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C3 |
| direct product | C17×C7⋊#157 |
| unambiguous semidirect product | C7⋊(C17×#157) |
| Fitting, socle, Hall | C32×C7×C17 ⋊ C4 |
| derived, Hall | C32×C7 ⋊ C4×C17 |
| Hall | C32×C17 ⋊ Dic7 |
| Hall | C7×C17 ⋊ #157 |
| Sylow | C32 ⋊ C17×Dic7 |
| Sylow | C7 ⋊ C17×#157 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C7⋊#157 |
| commutator, hypocenter | C32×C7 | C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C17 | C4 |
| prime radical | C7×C17×C3⋊D3 | C2 |
| cosocle | C7×C3⋊D3 | C2×C17 |
| LCS | G ▷ C32×C7 | |
| UCS | C1 ◁ C17 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 714 |
A minimal faithful permutation representation — 2 generators on 30 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21,23,22)(25,26)(27,28)(29,30);(18,20,23)(24,25,27,29,30,28,26)408 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C17×C7⋊#157, C17×C7⋊#4380, C17×C7⋊#4379, … |
| maximal normal subgroup of | C5×C17×C7⋊#157, C7×C17×C7⋊#157 |
| maximal quotient of | C5×C17×C7⋊#157, C17×C7⋊#4380, C17×C7⋊#4379, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4284, 113);