Finite Group DatabasebetaFinite Group Databasebeta| order | 1400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
No aliases for this group.
| Hall | C52×C7 ⋊ D4 |
| Sylow | C52 ⋊ D28 |
| Sylow | C7 ⋊ C22⋊(C5⋊D5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D7×C5⋊D5 |
| commutator, Fitting, socle, cosocle | C2×C52×C7 | C22 |
| hypocenter | C52×C7 | D4 |
| LCS | G ▷ C2×C52×C7 ▷ C52×C7 | |
| UCS | C1 ◁ C2 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 700 |
Polycyclic presentation:
2^3,5^2,7|b^2=c,b^a=bc,f^a=f^6,d^b=d^4,e^b=e^4137 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1400, 66);