Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | (C7⋊C9)⋊#92150 |
| derived, Hall | C7×C112 ⋊ C4×C9 |
| Hall | C112×C7⋊C9 ⋊ C4 |
| Hall | C7⋊#92150 ⋊ C9 |
| Sylow | C112 ⋊ Dic7⋊C9 |
| Hall | C7⋊C9 ⋊ #92150 |
| Sylow | C7 ⋊ C9×#92150 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | ΓL(1,𝔽8)⋊#92150 |
| commutator, hypocenter | C7×C112 | C4×C9 |
| Fitting, socle | C3×C7×C112 | C3×C4 |
| prime radical, cosocle | C3×C7×C11⋊D11 | C2×C3 |
| LCS | G ▷ C7×C112 | |
| UCS | C1 ◁ C3 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1386 |
Polycyclic presentation:
2,3,2,7,11^2,3|a^2=c,b^3=g,d^a=d^6,e^a=e^5f^7,f^a=ef^6,d^b=d^2,e^c=e^10,f^c=f^10492 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 150);