Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Hall | C3×C52 ⋊ C2×D4 |
| Sylow | C52 ⋊ D3×D4 |
| Sylow | C3 ⋊ D5×D20 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×D52 |
| commutator, Fitting, socle, cosocle | C2×C3×C52 | C23 |
| hypocenter | C3×C52 | C2×D4 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
248 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^4,3,5^2|b^2=d,c^2=d,b^a=bd,c^a=cd,f^a=f^4,g^b=g^4,e^c=e^281 conjugacy classes — view the full character table.
| maximal subgroup of | #72229792, D5×#6790, D3×D5×D20, … |
| maximal normal subgroup of | #72229792, D5×#6790, D3×D5×D20, … |
| maximal quotient of | #72260232 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 637);