Finite Group DatabasebetaFinite Group Databasebeta| order | 18876 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C11 |
| unambiguous semidirect product | D13⋊((C11⋊D11)⋊C3) |
| unambiguous semidirect product | #22628078⋊C2 |
| unambiguous semidirect product | ((C11⋊D11)⋊(C13⋊C3))⋊C2 |
| unambiguous semidirect product | (D13⋊(C112⋊C3))⋊C2 |
| Fitting, socle, derived, Hall | C112×C13 ⋊ C22×C3 |
| Hall | D13×C11⋊D11 ⋊ C3 |
| Hall | C13⋊(C112⋊C3) ⋊ C22 |
| Sylow | C112 ⋊ C2×D13⋊C3 |
| Sylow | C13 ⋊ C2×(C11⋊D11)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C112×C13 | C22×C3 |
| LCS | G ▷ C112×C13 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 429 |
Polycyclic presentation:
2^2,3,11^2,13|f^a=f^12,d^b=d^10,e^b=e^10,d^c=d^3e^9,e^c=de^7,f^c=f^3176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18876, 94);