Finite Group DatabasebetaFinite Group Databasebeta| order | 12100 |
| isoclinism | isoclinic class of #92150 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C52 · Schur multiplier (H2) = C5×C11 |
| direct product | C52×#92150 |
| Fitting, socle, Hall | C52×C112 ⋊ C4 |
| derived, Sylow | C112 ⋊ C4×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | #92150 |
| commutator, hypocenter | C112 | C4×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C112 | C4 |
| prime radical | C52×C11⋊D11 | C2 |
| cosocle | C11⋊D11 | C2×C52 |
| LCS | G ▷ C112 | |
| UCS | C1 ◁ C52 | |
144 conjugacy classes of subgroups.
850 conjugacy classes — view the full character table.
| maximal subgroup of | C52⋊C3×#92150, #92150⋊(C52⋊C3), C52×#13089721, … |
| maximal normal subgroup of | C52⋊C3×#92150, #92150⋊(C52⋊C3), C52×#92150⋊C3, … |
| maximal quotient of | C3×C52×#92150, C52×C3⋊#92150 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12100, 243);