Finite Group DatabasebetaFinite Group Databasebeta| order | 11900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊#13133352 |
| Fitting, socle, derived, Hall | C52×C7×C17 ⋊ C4 |
| Hall | C52×C17 ⋊ Dic7 |
| Hall | C52×C7 ⋊ Dic17 |
| Hall | C7×C17 ⋊ #1042 |
| Sylow | C52 ⋊ Dic119 |
| Sylow | C17 ⋊ C7⋊#1042 |
| Sylow | C7 ⋊ #13133352 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C7×C17 | C4 |
| prime radical, cosocle | C5×C7×D5×C17 | C2 |
| LCS | G ▷ C52×C7×C17 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,5^2,7,17|a^2=b,c^a=c^2,d^a=d^4,e^a=e^6,f^a=f^16,c^b=c^41193 conjugacy classes. The character table is too large to display.
| maximal subgroup of | ΓL(1,𝔽8)⋊#13133352, C3×C7⋊#13133352, C3⋊(C7⋊#13133352) |
| maximal normal subgroup of | ΓL(1,𝔽8)⋊#13133352, C3×C7⋊#13133352 |
| maximal quotient of | C3×C7⋊#13133352, C3⋊(C7⋊#13133352) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11900, 89);