Finite Group DatabasebetaFinite Group Databasebeta| order | 17552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C1097 ⋊ C2 |
| Sylow | C1097 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D1097 |
| commutator, cosocle | C4×C1097 | C22 |
| Frattini | C4 | C2×D1097 |
| Fitting | D4×C1097 | C2 |
| socle | C2×C1097 | D4 |
| hypercenter | D4 | D1097 |
| hypocenter | C1097 | D8 |
| LCS | G ▷ C4×C1097 ▷ C2×C1097 ▷ C1097 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8776 |
Polycyclic presentation:
2^4,1097|c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^10962747 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D8×D1097, C2×#31798149, #47975502, … |
| maximal normal subgroup of | D8×D1097, C2×#31798149, #47975502, … |
| maximal quotient of | #47975402, #47975403, #47975415, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17552, 25);