Finite Group DatabasebetaFinite Group Databasebeta| order | 17504 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C42×D547 |
| Fitting | C42×C547 ⋊ C2 |
| derived, Sylow | C547 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D547 |
| commutator, hypocenter | C547 | C2×C42 |
| Frattini | C22 | C22×D547 |
| Fitting | C42×C547 | C2 |
| socle, cosocle | C22×C547 | C23 |
| prime radical | C22×D547 | C22 |
| LCS | G ▷ C547 | |
| UCS | C1 ◁ C42 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8752 |
4400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×C8×D547, #97×D547, C4×#22576759, … |
| maximal normal subgroup of | C4×C8×D547, #97×D547, C4×#22576759, … |
| maximal quotient of | C42×Dic547, #95×D547, #46854846, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17504, 94);