Finite Group DatabasebetaFinite Group Databasebeta| order | 11100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C3⋊#16814887 |
| Fitting, socle, derived, Hall | C3×C52×C37 ⋊ C4 |
| Hall | C52×C37 ⋊ Dic3 |
| Hall | C3×C37 ⋊ #1039 |
| Hall | C3×C52 ⋊ #3866 |
| Sylow | C37 ⋊ C3⋊#1039 |
| Sylow | C52 ⋊ C3⋊#3866 |
| Sylow | C3 ⋊ #16814887 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C37 | C4 |
| prime radical, cosocle | C3×C52×D37 | C2 |
| LCS | G ▷ C3×C52×C37 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5^2,37|a^2=b,c^a=c^2,d^a=d^4,e^a=e^4,f^a=f^31,f^b=f^36753 conjugacy classes — view the full character table.
| maximal subgroup of | C9⋊#16814887, C3⋊#26012848, C3⋊#26012850, … |
| maximal normal subgroup of | C3⋊#26012848, C3⋊#26012850, C3⋊#26012827, … |
| maximal quotient of | C9⋊#16814887, C3×C3⋊#16814887, C3⋊(C3⋊#16814887) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11100, 186);