Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5×C11 |
| unambiguous semidirect product | C3⋊#27130990 |
| Fitting, socle, derived, Hall | C3×C52×C112 ⋊ C4 |
| Hall | C52×C112 ⋊ Dic3 |
| Hall | C3×C112 ⋊ #1039 |
| Sylow | C112 ⋊ C3⋊#1039 |
| Hall | C3×C52 ⋊ #92150 |
| Sylow | C52 ⋊ C3⋊#92150 |
| Sylow | C3 ⋊ #27130990 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C112 | C4 |
| prime radical, cosocle | C3×C52×C11⋊D11 | C2 |
| LCS | G ▷ C3×C52×C112 | |
| UCS | C1 | |
288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1650 |
Polycyclic presentation:
2^2,3,5^2,11^2|a^2=b,c^a=c^2,d^a=d^4,e^a=e^4,f^a=f^8g^8,g^a=f^7g^3,f^b=f^10,g^b=g^102328 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 922);