Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C7×C192 ⋊ C3×C4 |
| Hall | C7⋊#13089659 ⋊ C3 |
| Hall | C7×#11762245 ⋊ C4 |
| Hall | #11762245 ⋊ Dic7 |
| Sylow | C192 ⋊ C3×Dic7 |
| Sylow | C7 ⋊ #13089659⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C192 | C3×C4 |
| prime radical | C7×#14524206 | C2 |
| cosocle | C7×C19⋊D19 | C2×C3 |
| LCS | G ▷ C7×C192 | |
| UCS | C1 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 266 |
Polycyclic presentation:
2,3,2,7,19^2|a^2=c,d^a=d^6,e^a=e^4f^16,f^a=e^12f^15,e^b=e^7,f^b=f^7,e^c=e^18,f^c=f^18240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 192);