Finite Group DatabasebetaFinite Group Databasebeta| order | 30927 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, derived, Hall | C61×C169 ⋊ C3 |
| Sylow | C169 ⋊ C61⋊C3 |
| Sylow | C61 ⋊ C169⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C61×C169 | C3 |
| Frattini | C13 | #14558651 |
| socle | C13×C61 | C13⋊C3 |
| LCS | G ▷ C61×C169 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10309 |
Polycyclic presentation:
3,13,61,13|b^13=d^6,b^a=b^3d,c^a=c^13,d^a=d^33439 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30927, 4);