Finite Group DatabasebetaFinite Group Databasebeta| order | 700 |
| isoclinism | isoclinic class of (C5⋊D5)⋊D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C5⋊D5)⋊D7 |
| unambiguous semidirect product | D35⋊D5 |
| Fitting, socle, derived, Hall | C52×C7 ⋊ C22 |
| Sylow | C52 ⋊ C2×D7 |
| Sylow | C7 ⋊ D52 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7 | C22 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 70 |
Polycyclic presentation:
2^2,5^2,7|c^a=c^4,e^a=e^6,c^b=c^4,d^b=d^458 conjugacy classes — view the full character table.
| maximal subgroup of | #1043⋊D7, #13063833, #13063840, … |
| maximal normal subgroup of | #1043⋊D7, #13063833, #13063840, … |
| maximal quotient of | #13063792, #13063793, #13063794, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(700, 30);