Finite Group DatabasebetaFinite Group Databasebeta| order | 11900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C7⋊#13133334 |
| derived, Hall | C52×C7×C17 ⋊ C4 |
| Hall | C52×C17 ⋊ Dic7 |
| Hall | C52×C7 ⋊ Dic17 |
| Hall | C7×C17 ⋊ #1039 |
| Sylow | C52 ⋊ Dic119 |
| Sylow | C17 ⋊ C7⋊#1039 |
| Sylow | C7 ⋊ #13133334 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C5⋊D595 |
| commutator, hypocenter | C52×C7×C17 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C52×C7×C17 | C2 |
| LCS | G ▷ C52×C7×C17 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2,5^2,7,17,2|a^2=f,b^a=b^4,c^a=c^4,d^a=d^6,e^a=e^162978 conjugacy classes. The character table is too large to display.
| maximal subgroup of | ΓL(1,𝔽8)⋊#13133334, #49087674, #49087678, … |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊#13133334, #49087674, #49087678, … |
| maximal quotient of | C3⋊(C7⋊#13133334), C3×C7⋊#13133334 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11900, 47);