Finite Group DatabasebetaFinite Group Databasebeta| order | 1456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×Q8×C13 ⋊ C2 |
| Hall | C7×C13 ⋊ #41 |
| Sylow | C13 ⋊ #1161 |
| Sylow | C7 ⋊ #6131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D91 |
| commutator, socle, cosocle | C2×C7×C13 | C23 |
| Fitting | C7×Q8×C13 | C2 |
| hypercenter | Q8 | D91 |
| hypocenter | C7×C13 | #41 |
| LCS | G ▷ C2×C7×C13 ▷ C7×C13 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 728 |
Polycyclic presentation:
2^4,7,13|b^2=d,c^2=d,c^a=cd,e^a=e^6,f^a=f^12,c^b=cd235 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1456, 163);