Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of #1043⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #6033⋊C3 |
| derived, Sylow | C52 ⋊ C3×C8 |
| Hall | #6033 ⋊ C3 |
| Hall | C52⋊C3 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #1043⋊C3 |
| commutator, hypocenter | C52 | C3×C8 |
| Fitting, socle | C2×C52 | C3×C4 |
| prime radical | C2×C52⋊C3 | C4 |
| cosocle | #1039 | C2×C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2 | |
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^2,f^a=f^2,e^b=ef,f^b=e^2f^3,e^c=e^4,f^c=f^428 conjugacy classes — view the full character table.
| maximal subgroup of | #11925275, #87822⋊C3, #11925277, … |
| maximal normal subgroup of | #11925275, #87822⋊C3, #11925277, … |
| maximal quotient of | #87764⋊C3, C2×#6033⋊C3, #6033⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 56);