Finite Group DatabasebetaFinite Group Databasebeta| order | 952 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C7 · Schur multiplier (H2) = C2 |
| direct product | C4×C7×D17 |
| Fitting | C4×C7×C17 ⋊ C2 |
| derived, Sylow | C17 ⋊ C2×C4×C7 |
| Hall | C7×C17 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C7 | D17 |
| commutator, hypocenter | C17 | C2×C4×C7 |
| Frattini | C2 | C2×C7×D17 |
| Fitting | C4×C7×C17 | C2 |
| socle | C2×C7×C17 | C22 |
| prime radical | C2×C7×D17 | C2 |
| cosocle | C2×C17 | C22×C7 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C4×C7 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 476 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D17×C7⋊C8, #14274027, C7×C8×D17, … |
| maximal normal subgroup of | D17×C7⋊C8, #14274027, C7×C8×D17, … |
| maximal quotient of | C7×C8×D17, C7×#63218, C4×C7×Dic17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(952, 15);