Finite Group DatabasebetaFinite Group Databasebeta| order | 11948 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C103⋊#1181 |
| Fitting, socle, derived, Hall | C29×C103 ⋊ C4 |
| Sylow | C103 ⋊ #1181 |
| Sylow | C29 ⋊ Dic103 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C103 | C4 |
| prime radical, cosocle | D29×C103 | C2 |
| LCS | G ▷ C29×C103 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,29,103|a^2=b,c^a=c^17,d^a=d^102,c^b=c^28827 conjugacy classes — view the full character table.
| maximal subgroup of | (C103⋊C3)⋊#1181, C3×C103⋊#1181, C3⋊(C103⋊#1181) |
| maximal normal subgroup of | (C103⋊C3)⋊#1181, C3×C103⋊#1181 |
| maximal quotient of | C3×C103⋊#1181, C3⋊(C103⋊#1181) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11948, 7);