Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C52⋊C3 ⋊ D8 |
| Sylow | C52 ⋊ #213 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10597080 |
| commutator, cosocle | C4×C52⋊C3 | C22 |
| Frattini, hypercenter | C4 | #3874⋊C2 |
| Fitting | C4×C52 | C2×D3 |
| socle | C2×C52 | #67 |
| hypocenter | C52⋊C3 | D8 |
| LCS | G ▷ C4×C52⋊C3 ▷ C2×C52⋊C3 ▷ C52⋊C3 | |
| UCS | C1 ◁ C2 ◁ C4 | |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^4,3,5^2|b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^2,f^a=g,g^a=f,e^b=e^2,f^b=g^4,g^b=f^4,f^e=g,g^e=f^4g^438 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 219);