Finite Group DatabasebetaFinite Group Databasebeta| order | 17504 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C547 ⋊ C2 |
| Sylow | C547 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D547 |
| commutator, socle | C2×C547 | C22×C4 |
| Fitting | M16×C547 | C2 |
| prime radical | #22576776 | C2 |
| cosocle | C4×C547 | C23 |
| hypercenter | M16 | D547 |
| hypocenter | C547 | #131 |
| LCS | G ▷ C2×C547 ▷ C547 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8752 |
Polycyclic presentation:
2^5,547|a^2=d,d^2=e,f^a=f^546,c^b=ce,f^c=f^5462750 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46855115, #46855117, #46855120, … |
| maximal normal subgroup of | #46855115, #46855117, #46855120, … |
| maximal quotient of | #46854958, #46854959, #46854966, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17504, 154);