Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of (C5⋊D5)⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | #6029⋊C3 |
| derived, Sylow | C52 ⋊ C3×C8 |
| Hall | #6029 ⋊ C3 |
| Hall | C52⋊C3 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | (C5⋊D5)⋊C3 |
| commutator, hypocenter | C52 | C3×C8 |
| Fitting, cosocle | C4×C52 | C2×C3 |
| socle | C2×C52 | C3×C4 |
| prime radical | C2×C52⋊C3 | C4 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C4 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2,3,2^2,5^2|a^2=c,c^2=d,e^a=e^4,f^a=f^4,e^b=e^3f^3,f^b=e^4f40 conjugacy classes — view the full character table.
| maximal subgroup of | #11925000, #87764⋊C3, #11925002, … |
| maximal normal subgroup of | #11925000, #87764⋊C3, #11925002, … |
| maximal quotient of | #87756⋊C3, C2×#6029⋊C3, #6029⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 46);