Finite Group DatabasebetaFinite Group Databasebeta| order | 11100 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×#16814878 |
| Fitting, socle, Hall | C3×C52×C37 ⋊ C4 |
| derived, Hall | C52×C37 ⋊ C3×C4 |
| Hall | C3×C37 ⋊ #1043 |
| Hall | C3×C52 ⋊ #3866 |
| Sylow | C37 ⋊ C3×#1043 |
| Sylow | C52 ⋊ C3×#3866 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16814878 |
| commutator, hypocenter | C52×C37 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C37 | C4 |
| prime radical | C3×C5⋊D185 | C2 |
| cosocle | C5⋊D185 | C2×C3 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 ◁ C3 | |
96 conjugacy classes of subgroups.
705 conjugacy classes — view the full character table.
| maximal subgroup of | #45685946, #45685968, #45685970, … |
| maximal normal subgroup of | #45685946, #45685968, #45685970, … |
| maximal quotient of | C9×#16814878, C32×#16814878, C3×C3⋊#16814878 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11100, 149);