Finite Group DatabasebetaFinite Group Databasebeta| order | 952 |
| isoclinism | isoclinic class of D119 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#3622 |
| derived, Hall | C7×C17 ⋊ C8 |
| Sylow | C17 ⋊ C7⋊C8 |
| Sylow | C7 ⋊ #3622 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | D119 |
| commutator, hypocenter | C7×C17 | C8 |
| Fitting, cosocle | C4×C7×C17 | C2 |
| socle, prime radical | C2×C7×C17 | C4 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C4 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 952 |
Polycyclic presentation:
2^3,7,17|a^2=b,b^2=c,d^a=d^6,e^a=e^16244 conjugacy classes — view the full character table.
| maximal subgroup of | D17×C7⋊C8, D7×#3622, #14274027, … |
| maximal normal subgroup of | D17×C7⋊C8, D7×#3622, #14274027, … |
| maximal quotient of | C7⋊#63214, C2×C7⋊#3622 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(952, 3);