Finite Group DatabasebetaFinite Group Databasebeta| order | 17552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C23×D1097 |
| unambiguous semidirect product | C1097⋊C24 |
| unambiguous semidirect product | (C2×C1097)⋊C23 |
| Fitting, socle | C23×C1097 ⋊ C2 |
| derived, Sylow | C1097 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D1097 |
| commutator, cosocle, hypocenter | C1097 | C24 |
| Frattini | C1 | G |
| Fitting, socle | C23×C1097 | C2 |
| LCS | G ▷ C1097 | |
| UCS | C1 ◁ C23 | |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8776 |
4400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊C4×D1097, C2×#31798141, #47975450, … |
| maximal normal subgroup of | C22⋊C4×D1097, C2×#31798141, #47975450, … |
| maximal quotient of | C22×C4×D1097, C23×Dic1097, C2×D4×D1097, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17552, 42);