Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C11 |
| unambiguous semidirect product | C11⋊(C11⋊#1043) |
| Fitting, socle, derived, Hall | C52×C112 ⋊ C4 |
| Sylow | C112 ⋊ #1043 |
| Sylow | C52 ⋊ C11⋊Dic11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C112 | C4 |
| prime radical, cosocle | C112×C5⋊D5 | C2 |
| LCS | G ▷ C52×C112 | |
| UCS | C1 | |
336 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,11^2|a^2=b,c^a=c^2,d^a=d^2,e^a=e^10,f^a=f^10,c^b=c^4,d^b=d^4850 conjugacy classes — view the full character table.
| maximal subgroup of | #49137570, C11⋊(C11⋊(#1043⋊C3)), #49137618, … |
| maximal normal subgroup of | #49137570, C11⋊(C11⋊(#1043⋊C3)), #49137618, … |
| maximal quotient of | C3×C11⋊(C11⋊#1043), C3⋊(C11⋊(C11⋊#1043)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 255);