Finite Group DatabasebetaFinite Group Databasebeta| order | 30324 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C19 |
| unambiguous semidirect product | C7⋊#16864578 |
| Fitting, socle, Hall | C7×C192 ⋊ Dic3 |
| derived, Hall | C7×#11762246 ⋊ C4 |
| Hall | #11762246 ⋊ Dic7 |
| Sylow | C192 ⋊ Dic21 |
| Sylow | C7 ⋊ #16864578 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, hypocenter | C7×#11762246 | C4 |
| Fitting, socle | C7×C192 | Dic3 |
| prime radical, cosocle | C7×#14524207 | C2 |
| LCS | G ▷ C7×#11762246 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 266 |
Polycyclic presentation:
2^2,3,7,19^2|a^2=b,c^a=c^2,d^a=d^6,e^a=e^8f^11,f^a=ef^11,e^b=e^18,f^b=f^18,e^c=e^7f^13,f^c=f^11234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30324, 191);