Finite Group DatabasebetaFinite Group Databasebeta| order | 29694 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C101⋊#64422 |
| Fitting, socle, derived, Hall | C72×C101 ⋊ C2×C3 |
| Hall | C101×#3862 ⋊ C2 |
| Hall | C7×D707 ⋊ C3 |
| Hall | #3862 ⋊ D101 |
| Sylow | C101 ⋊ #64422 |
| Sylow | C72 ⋊ C3×D101 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C101 | C2×C3 |
| LCS | G ▷ C72×C101 | |
| UCS | C1 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4242 |
Polycyclic presentation:
2,3,7^2,101|d^a=d^6,e^a=e^100,c^b=c^2,d^b=d^4967 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29694, 29);