Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived | C5×C112 ⋊ C4×C5 |
| Hall | C5×#10597244 ⋊ C4 |
| Sylow | C112 ⋊ C5×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C112 | C4×C5 |
| prime radical | D5×#10597244 | C2 |
| cosocle | D5×C112 | C2×C5 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,2,5,11^2|a^2=c,d^a=d^2,e^a=e^10,e^b=e^4,f^b=f^5,d^c=d^479 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#27130899, C3⋊#27130899 |
| maximal normal subgroup of | C3×#27130899 |
| maximal quotient of | C3×#27130899, C3⋊#27130899 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 178);