Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C52 ⋊ C4⋊C4 |
| Sylow | C52 ⋊ Dic3⋊C4 |
| Sylow | C3 ⋊ #87825 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | AGL(1,𝔽5)×D15 |
| commutator, Fitting, socle | C2×C3×C52 | C2×C4 |
| prime radical, cosocle | C2×C3×C5×D5 | C22 |
| hypocenter | C3×C52 | C4⋊C4 |
| LCS | G ▷ C2×C3×C52 ▷ C3×C52 | |
| UCS | C1 ◁ C2 | |
110 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 240 |
Polycyclic presentation:
2^4,3,5^2|a^2=d,b^2=c,b^a=bd,e^a=e^2,g^a=g^4,f^b=f^2,f^c=f^484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 576);