Finite Group DatabasebetaFinite Group Databasebeta| order | 17456 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C1091 ⋊ C2 |
| Sylow | C1091 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D1091 |
| commutator, socle, cosocle | C2×C1091 | C23 |
| Fitting | Q8×C1091 | C2 |
| hypercenter | Q8 | D1091 |
| hypocenter | C1091 | #41 |
| LCS | G ▷ C2×C1091 ▷ C1091 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8728 |
Polycyclic presentation:
2^4,1091|c^2=d,b^a=bd,e^a=e^1090,e^b=e^1090,e^c=e^10902735 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46853455, #46853457, #46853461, … |
| maximal normal subgroup of | #46853455, #46853457, #46853461, … |
| maximal quotient of | #46853392, #46853396, Q8×Dic1091, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17456, 41);