Finite Group DatabasebetaFinite Group Databasebeta| order | 26901 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C72×C61 ⋊ C9 |
| Sylow | C61 ⋊ #89204 |
| Sylow | C72 ⋊ C61⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #22582226 |
| commutator, hypocenter | C72×C61 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C72×C61 | C3 |
| LCS | G ▷ C72×C61 | |
| UCS | C1 ◁ C3 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26901 |
Polycyclic presentation:
3,7^2,61,3|a^3=e,b^a=b^4,c^a=c^4,d^a=d^472997 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26901, 19);