Finite Group DatabasebetaFinite Group Databasebeta| order | 1456 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C7×C13 ⋊ D8 |
| Sylow | C13 ⋊ #1141 |
| Sylow | C7 ⋊ D104 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10624411 |
| commutator, Fitting, cosocle | C4×C7×C13 | C22 |
| Frattini, hypercenter | C4 | D7×D13 |
| socle | C2×C7×C13 | D4 |
| hypocenter | C7×C13 | D8 |
| LCS | G ▷ C4×C7×C13 ▷ C2×C7×C13 ▷ C7×C13 | |
| UCS | C1 ◁ C2 ◁ C4 | |
44 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 728 |
Polycyclic presentation:
2^4,7,13|b^2=cd,c^2=d,b^a=bc,c^a=cd,f^a=f^12,e^b=e^6142 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1456, 14);