Finite Group DatabasebetaFinite Group Databasebeta| order | 26307 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C37×C79 ⋊ C9 |
| Sylow | C79 ⋊ #66524 |
| Sylow | C37 ⋊ C79⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #22578530 |
| commutator, hypocenter | C37×C79 | C9 |
| Fitting, socle, prime radical, cosocle | C3×C37×C79 | C3 |
| LCS | G ▷ C37×C79 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 26307 |
Polycyclic presentation:
3,37,79,3|a^3=d,b^a=b^26,c^a=c^232931 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26307, 5);