Finite Group DatabasebetaFinite Group Databasebeta| order | 600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C52 ⋊ D4 |
| Sylow | C52 ⋊ D12 |
| Sylow | C3 ⋊ #6037 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D15⋊D5 |
| commutator, Fitting, socle, cosocle | C2×C3×C52 | C22 |
| hypocenter | C3×C52 | D4 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^3,3,5^2|b^2=c,b^a=bc,d^a=d^2,e^a=e^4,e^b=e^4,f^b=f^457 conjugacy classes — view the full character table.
| maximal subgroup of | #11925399, #11925400, #11925405, … |
| maximal normal subgroup of | #11925399, #11925400, #11925405, … |
| maximal quotient of | #11925154, #11925157, #11925159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(600, 109);