Finite Group DatabasebetaFinite Group Databasebeta| order | 18772 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D247⋊D19 |
| unambiguous semidirect product | (C19⋊D19)⋊D13 |
| Fitting, socle, derived, Hall | C13×C192 ⋊ C22 |
| Sylow | C192 ⋊ C2×D13 |
| Sylow | C13 ⋊ D192 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C192 | C22 |
| LCS | G ▷ C13×C192 | |
| UCS | C1 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 494 |
Polycyclic presentation:
2^2,13,19^2|c^a=c^12,d^a=d^18,d^b=d^18,e^b=e^181213 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18772, 28);