Finite Group DatabasebetaFinite Group Databasebeta| order | 17488 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D1093⋊C8 |
| derived, Sylow | C1093 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #17983840 |
| commutator, hypocenter | C1093 | C2×C8 |
| Frattini | C2 | C2×#17983840 |
| Fitting | C4×C1093 | C4 |
| socle | C2×C1093 | C2×C4 |
| prime radical | C2×D1093 | C4 |
| cosocle | Dic1093 | C22 |
| LCS | G ▷ C1093 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8744 |
Polycyclic presentation:
2^4,1093|a^2=c,c^2=d,e^a=e^563,e^b=e^1092,e^c=e^10921108 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#17983840, #46854161, #46854169, … |
| maximal normal subgroup of | C8×#17983840, #46854161, #46854169, … |
| maximal quotient of | C4×#22576727, #46854164, #46854174, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17488, 48);