Finite Group DatabasebetaFinite Group Databasebeta| order | 1372 |
| isoclinism | isoclinic class of ((C7⋊D7)⋊C7)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | ((C7⋊D7)⋊C7)⋊C2 |
| unambiguous semidirect product | #10621859⋊C2 |
| Fitting, derived, Sylow | H(3,𝔽7) ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | H(3,𝔽7) | C22 |
| Frattini, socle | C7 | D72 |
| LCS | G ▷ H(3,𝔽7) | |
| UCS | C1 | |
47 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 49 |
Polycyclic presentation:
2^2,7^3|d^a=d^6,e^a=e^6,c^b=c^6,e^b=e^6,d^c=de31 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1372, 16);