Finite Group DatabasebetaFinite Group Databasebeta| order | 18300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #1043⋊(C61⋊C3) |
| Fitting, socle, derived, Hall | C52×C61 ⋊ C3×C4 |
| Hall | C61×#1043 ⋊ C3 |
| Hall | C52⋊(C61⋊C3) ⋊ C4 |
| Hall | #1043 ⋊ C61⋊C3 |
| Sylow | C61 ⋊ #1043⋊C3 |
| Sylow | C52 ⋊ C4×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C61 | C3×C4 |
| prime radical | (C5⋊D5)⋊(C61⋊C3) | C2 |
| cosocle | C5⋊D5×C61 | C2×C3 |
| LCS | G ▷ C52×C61 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 915 |
Polycyclic presentation:
2,3,2,5^2,61|a^2=c,d^a=d^3,e^a=e^3,d^b=de^2,e^b=de^3,f^b=f^13,d^c=d^4,e^c=e^4214 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18300, 178);