Finite Group DatabasebetaFinite Group Databasebeta| order | 20972 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C7⋊D7)⋊D107 |
| unambiguous semidirect product | D749⋊D7 |
| Fitting, socle, derived, Hall | C72×C107 ⋊ C22 |
| Sylow | C107 ⋊ D72 |
| Sylow | C72 ⋊ C2×D107 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C107 | C22 |
| LCS | G ▷ C72×C107 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1498 |
Polycyclic presentation:
2^2,7^2,107|c^a=c^6,e^a=e^106,c^b=c^6,d^b=d^61403 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20972, 22);