Finite Group DatabasebetaFinite Group Databasebeta| order | 17552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C1097 ⋊ C2 |
| Sylow | C1097 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D1097 |
| commutator, socle | C2×C1097 | C2×C4 |
| Fitting | C8×C1097 | C2 |
| prime radical | C2×D1097 | C4 |
| cosocle | C4×C1097 | C22 |
| hypercenter | C8 | D1097 |
| hypocenter | C1097 | M16 |
| LCS | G ▷ C2×C1097 ▷ C1097 | |
| UCS | C1 ◁ C4 ◁ C8 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8776 |
Polycyclic presentation:
2^4,1097|a^2=c,c^2=d,b^a=bd,e^b=e^10964394 conjugacy classes. The character table is too large to display.
| maximal subgroup of | M16×D1097, C2×#31798147, #47975488, … |
| maximal normal subgroup of | M16×D1097, C2×#31798147, #47975488, … |
| maximal quotient of | #47975392, #47975394, #47975411, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17552, 23);