Finite Group DatabasebetaFinite Group Databasebeta| order | 952 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×C22⋊D7 |
| unambiguous semidirect product | C22⋊(D7×C17) |
| Fitting | C22×C7×C17 ⋊ C2 |
| Hall | C7×C17 ⋊ D4 |
| Sylow | C7 ⋊ D4×C17 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C17 | C2×D7 |
| commutator, cosocle | C2×C7 | C22×C17 |
| Frattini | C2 | C2×D7×C17 |
| Fitting | C22×C7×C17 | C2 |
| socle | C2×C7×C17 | C22 |
| hypercenter | C22×C17 | D7 |
| hypocenter | C7 | D4×C17 |
| LCS | G ▷ C2×C7 ▷ C7 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C17 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 476 |
289 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14274144, #14274146, D17×C22⋊D7, … |
| maximal normal subgroup of | #14274144, #14274146, D17×C22⋊D7, … |
| maximal quotient of | C17×Dic7⋊C4, C17×(C2×D7)⋊C4, C17×#1141, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(952, 23);