Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| isoclinism | isoclinic class of #3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C52⋊C3 ⋊ C8 |
| Sylow | C52 ⋊ C3⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #3874 |
| commutator, hypocenter | C52⋊C3 | C8 |
| Fitting | C4×C52 | D3 |
| socle | C2×C52 | Dic3 |
| prime radical | C2×C52⋊C3 | C4 |
| cosocle | C4×C52⋊C3 | C2 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C4 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^3,3,5^2|a^2=b,b^2=c,d^a=d^2,e^a=e^2f,f^a=e^2f^3,e^d=e^2f^4,f^d=e^2f^252 conjugacy classes — view the full character table.
| maximal subgroup of | #11925002, #11925003, #11925007, … |
| maximal normal subgroup of | #11925002, #11925003, #11925007, … |
| maximal quotient of | #11924973, C2×#10597064, #14267857, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 45);