Finite Group DatabasebetaFinite Group Databasebeta| order | 1400 |
| isoclinism | isoclinic class of (C5⋊D5)⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Hall | C52×C7 ⋊ C2×C4 |
| Sylow | C52 ⋊ C4×D7 |
| Sylow | C7 ⋊ D5×Dic5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C5⋊D5)⋊D7 |
| commutator, hypocenter | C52×C7 | C2×C4 |
| Fitting, socle, cosocle | C2×C52×C7 | C22 |
| prime radical | C2×C5×D35 | C2 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C2 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
Polycyclic presentation:
2^3,5^2,7|b^2=c,d^a=d^4,f^a=f^6,d^b=d^4,e^b=e^4116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1400, 81);