Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived | C5×C112 ⋊ C4×C5 |
| Hall | C5×#10597245 ⋊ C4 |
| Sylow | C112 ⋊ C5×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊#11925896 |
| commutator, hypocenter | C5×C112 | C4×C5 |
| Fitting, socle, cosocle | C2×C5×C112 | C2×C5 |
| prime radical | C2×C5×#10597245 | C2 |
| LCS | G ▷ C5×C112 | |
| UCS | C1 ◁ C2 | |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2,5^2,11^2,2|a^2=f,c^a=c^4,d^a=d^10,d^b=d^4,e^b=e^3166 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#27130855, C3⋊#27130855 |
| maximal normal subgroup of | C3×#27130855 |
| maximal quotient of | C3×#27130855, C3⋊#27130855 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 134);