Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C52 ⋊ Q8 |
| Sylow | C52 ⋊ Dic6 |
| Sylow | C3 ⋊ #6039 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×D15 |
| commutator, Fitting, socle, prime radical, cosocle | C2×C3×C52 | C22 |
| hypocenter | C3×C52 | Q8 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^3,3,5^2|a^2=c,b^2=c,b^a=bc,d^a=d^2,f^a=f^4,e^b=e^469 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1204, #11925431, D3×#6039, … |
| maximal normal subgroup of | D5×#1204, #11925431, D3×#6039, … |
| maximal quotient of | #11925146, #11925147, #11925148, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 105);