Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C52⋊C3 ⋊ #41 |
| Sylow | C52 ⋊ #237 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#3874⋊C2 |
| commutator, cosocle | C2×C52⋊C3 | C23 |
| Fitting | C4×C52 | C2×D3 |
| socle | C2×C52 | C22×D3 |
| hypercenter | C4 | #3874⋊C2 |
| hypocenter | C52⋊C3 | #41 |
| LCS | G ▷ C2×C52⋊C3 ▷ C52⋊C3 | |
| UCS | C1 ◁ C2 ◁ C4 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^4,3,5^2|b^2=d,c^2=d,b^a=bd,e^a=e^2,f^a=fg,g^a=g^4,c^b=cd,e^b=e^2,f^b=f^4g^4,f^e=g,g^e=f^4g^441 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 511);