Finite Group DatabasebetaFinite Group Databasebeta| order | 30492 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #14546095⋊D7 |
| derived, Hall | C7×C112⋊C9 ⋊ C22 |
| Hall | C112⋊C9 ⋊ C2×D7 |
| Hall | C7×C112 ⋊ C2×D9 |
| Sylow | C112 ⋊ D7×D9 |
| Sylow | C7 ⋊ #14546095⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C7×C112⋊C9 | C22 |
| Frattini | C3 | #10624391⋊D7 |
| Fitting, socle | C3×C7×C112 | C2×D3 |
| LCS | G ▷ C7×C112⋊C9 | |
| UCS | C1 | |
108 conjugacy classes of subgroups; only the 17 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 17 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 693 |
Polycyclic presentation:
2^2,3,7,11^2,3|c^3=g^2,d^a=d^6,e^a=e^10,f^a=f^10,c^b=c^2g,e^b=e^3f^10,f^b=e^8f^8,g^b=g^2,e^c=e^2f^10,f^c=e^7f^8300 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 154);