Finite Group DatabasebetaFinite Group Databasebeta| order | 24206 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | C7⋊D1729 |
| unambiguous semidirect product | C13⋊(C7⋊D133) |
| unambiguous semidirect product | C19⋊(C7⋊D91) |
| Fitting, socle, derived, Hall | C72×C13×C19 ⋊ C2 |
| Hall | C72×C19 ⋊ D13 |
| Hall | C72×C13 ⋊ D19 |
| Hall | C13×C19 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D247 |
| Sylow | C19 ⋊ C7⋊D91 |
| Sylow | C13 ⋊ C7⋊D133 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C13×C19 | C2 |
| LCS | G ▷ C72×C13×C19 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12103 |
Polycyclic presentation:
2,7^2,13,19|b^a=b^6,c^a=c^6,d^a=d^12,e^a=e^186053 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24206, 20);