Finite Group DatabasebetaFinite Group Databasebeta| order | 16317 |
| isoclinism | isoclinic class of C37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C72×C9 · Schur multiplier (H2) = C7 |
| direct product | C72×#66524 |
| derived, Sylow | C37 ⋊ C72×C9 |
| Hall | C72×C37 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C72 | C37⋊C3 |
| commutator, hypocenter | C37 | C72×C9 |
| Frattini | C3 | C72×C37⋊C3 |
| Fitting, socle, prime radical | C3×C72×C37 | C3 |
| cosocle | C3×C37 | C3×C72 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3×C72 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16317 |
2205 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C72×#66524⋊C2, C7×#66524⋊D7, C7×D7×#66524, … |
| maximal normal subgroup of | C72×#66524⋊C2, C7×#66524⋊D7, C7×D7×#66524, … |
| maximal quotient of | C2×C72×#66524 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16317, 16);