Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C52⋊C3 ⋊ M16 |
| Sylow | C52 ⋊ ΓL(1,𝔽25) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #64480⋊C2 |
| commutator | C2×C52⋊C3 | C2×C4 |
| Fitting, socle | C2×C52 | C4×D3 |
| prime radical | C2×#3874 | C4 |
| cosocle | #1039⋊C3 | C22 |
| hypocenter | C52⋊C3 | M16 |
| LCS | G ▷ C2×C52⋊C3 ▷ C52⋊C3 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 120 |
Polycyclic presentation:
2^4,3,5^2|a^2=c,b^2=d,c^2=d,b^a=bd,f^a=f^3,g^a=g^3,e^b=e^2,f^b=g^2,g^b=f^3,f^c=f^4,g^c=g^4,f^e=f^4g^2,g^e=f^226 conjugacy classes — view the full character table.
| maximal subgroup of | ΣL(2,𝔽25) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 488);