Finite Group DatabasebetaFinite Group Databasebeta| order | 1400 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C52×C7 ⋊ D4 |
| Sylow | C52 ⋊ D28 |
| Sylow | C7 ⋊ #6038 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×D35 |
| commutator, Fitting, socle, cosocle | C2×C52×C7 | C22 |
| hypocenter | C52×C7 | D4 |
| LCS | G ▷ C2×C52×C7 ▷ C52×C7 | |
| UCS | C1 ◁ C2 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 140 |
Polycyclic presentation:
2^3,5^2,7|b^2=c,b^a=bc,d^a=d^4,f^a=f^6,e^b=e^4149 conjugacy classes — view the full character table.
| maximal subgroup of | #72243078, #72243100, D7×#6038, … |
| maximal normal subgroup of | #72243078, #72243100, D7×#6038, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1400, 78);