Finite Group DatabasebetaFinite Group Databasebeta| order | 1456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C7×C13 ⋊ C22 |
| Hall | C7×C13 ⋊ C2×D4 |
| Sylow | C13 ⋊ D4×D7 |
| Sylow | C7 ⋊ D4×D13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D7×D13 |
| commutator, socle, cosocle | C2×C7×C13 | C23 |
| Fitting | C22×C7×C13 | C22 |
| hypercenter | C22 | D7×D13 |
| hypocenter | C7×C13 | C2×D4 |
| LCS | G ▷ C2×C7×C13 ▷ C7×C13 | |
| UCS | C1 ◁ C2 ◁ C22 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 364 |
Polycyclic presentation:
2^4,7,13|c^a=cd,f^a=f^12,c^b=cd,e^b=e^6127 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1456, 135);