Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| isoclinism | isoclinic class of D72 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C72 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C4 | D72 |
| commutator, hypocenter | C72 | C4×C8 |
| Fitting, cosocle | C2×C4×C72 | C22 |
| socle, prime radical | C22×C72 | C2×C4 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C2×C4 | |
133 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
Polycyclic presentation:
2^5,7^2|a^2=d,b^2=c,c^2=e,d^2=e,g^a=g^6,f^b=f^6200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 211);