Finite Group DatabasebetaFinite Group Databasebeta| order | 30268 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(Dic47⋊C23) |
| unambiguous semidirect product | (C47⋊C23)⋊Dic7 |
| unambiguous semidirect product | Dic329⋊C23 |
| derived, Hall | C7×C47 ⋊ C4×C23 |
| Hall | C7×C47⋊C23 ⋊ C4 |
| Hall | Dic329 ⋊ C23 |
| Hall | C47⋊C23 ⋊ Dic7 |
| Sylow | C47 ⋊ C23×Dic7 |
| Sylow | C7 ⋊ Dic47⋊C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊AGL(1,𝔽47) |
| commutator, hypocenter | C7×C47 | C4×C23 |
| Fitting, socle, cosocle | C2×C7×C47 | C2×C23 |
| prime radical | C2×C7×C47⋊C23 | C2 |
| LCS | G ▷ C7×C47 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1316 |
Polycyclic presentation:
2,7,23,47,2|a^2=e,b^a=b^6,d^a=d^46,d^c=d^25244 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30268, 12);