Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5×C11 |
| unambiguous semidirect product | C11⋊(C11⋊#1039) |
| derived, Hall | C52×C112 ⋊ C4 |
| Sylow | C112 ⋊ #1039 |
| Sylow | C52 ⋊ C11⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊(C5⋊(C11⋊D11)) |
| commutator, hypocenter | C52×C112 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C52×C112 | C2 |
| LCS | G ▷ C52×C112 | |
| UCS | C1 ◁ C2 | |
336 conjugacy classes of subgroups.
Polycyclic presentation:
2,5^2,11^2,2|a^2=f,b^a=b^4,c^a=c^4,d^a=d^10,e^a=e^103028 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49137287, C11⋊(C11⋊(#1039⋊C3)), #49137296, … |
| maximal normal subgroup of | #49137287, C11⋊(C11⋊(#1039⋊C3)), #49137296, … |
| maximal quotient of | C3⋊(C11⋊(C11⋊#1039)), C3×C11⋊(C11⋊#1039) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 154);