Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | #92150⋊(C7⋊C9) |
| derived, Hall | C7×C112 ⋊ C4×C9 |
| Hall | C7⋊(C112⋊C9) ⋊ C4 |
| Hall | C7×#92150 ⋊ C9 |
| Hall | #92150 ⋊ C7⋊C9 |
| Sylow | C112 ⋊ C4×C7⋊C9 |
| Sylow | C7 ⋊ #92150⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #92150⋊ΓL(1,𝔽8) |
| 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 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1386 |
Polycyclic presentation:
2,3,2,7,11^2,3|a^2=c,b^3=g,e^a=e^8f^8,f^a=e^7f^3,d^b=d^2,e^b=e^3f^9,f^b=ef^7,e^c=e^10,f^c=f^10270 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 152);