Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, Hall | C112×C25 ⋊ Dic3 |
| derived, Hall | C25×C112⋊C3 ⋊ C4 |
| Hall | C112⋊C3 ⋊ #1035 |
| Sylow | C112 ⋊ C3⋊#1035 |
| Sylow | C25 ⋊ #13089712 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, hypocenter | C25×C112⋊C3 | C4 |
| Frattini | C5 | #20300037 |
| Fitting | C112×C25 | Dic3 |
| socle | C5×C112 | ΓL(1,𝔽16) |
| prime radical, cosocle | D25×C112⋊C3 | C2 |
| LCS | G ▷ C25×C112⋊C3 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 825 |
Polycyclic presentation:
2^2,3,5,11^2,5|a^2=b,d^5=g,c^a=c^2,d^a=d^2g,e^a=e^2f^10,f^a=e^3f^9,g^a=g^2,d^b=d^4g^4,g^b=g^4,e^c=e^2f^10,f^c=e^7f^8334 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 251);