Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C7×C361 ⋊ C3×C4 |
| Hall | Dic2527 ⋊ C3 |
| Hall | #21439055 ⋊ C4 |
| Sylow | C361 ⋊ ΓL(1,𝔽8)⋊C4 |
| Sylow | C7 ⋊ (C361⋊C3)⋊C4 |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10108 |
Polycyclic presentation:
2,3,7,19,2,19|a^2=e,d^19=f^18,c^a=c^6,d^a=d^18f,f^a=f^18,c^b=c^2,d^b=d^7f^4,f^b=f^7854 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 12);