Finite Group DatabasebetaFinite Group Databasebeta| order | 30276 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C292 ⋊ C22 |
| Sylow | C292 ⋊ C2×C3⋊D3 |
| Sylow | C32 ⋊ D292 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C292 | C22 |
| LCS | G ▷ C32×C292 | |
| UCS | C1 | |
288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 522 |
Polycyclic presentation:
2^2,3^2,29^2|c^a=c^2,d^a=d^2,e^a=e^28,e^b=e^28,f^b=f^281944 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30276, 135);