Finite Group DatabasebetaFinite Group Databasebeta| order | 36900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊#16861519) |
| Fitting, socle, derived, Hall | C32×C52×C41 ⋊ C4 |
| Hall | C52×C41 ⋊ C3⋊Dic3 |
| Hall | C32×C41 ⋊ #1043 |
| Hall | C32×C52 ⋊ #4223 |
| Sylow | C41 ⋊ C3⋊(C3⋊#1043) |
| Sylow | C52 ⋊ C3⋊(C3⋊#4223) |
| Sylow | C32 ⋊ #16861519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C52×C41 | C4 |
| prime radical, cosocle | C32×C5⋊D205 | C2 |
| LCS | G ▷ C32×C52×C41 | |
| UCS | C1 | |
288 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9225 |
Polycyclic presentation:
2^2,3^2,5^2,41|a^2=b,c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^2,g^a=g^9,e^b=e^4,f^b=f^4,g^b=g^402316 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36900, 597);