Finite Group DatabasebetaFinite Group Databasebeta| order | 16736 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C523 ⋊ C2 |
| Sylow | C523 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D523 |
| commutator, socle | C2×C523 | C22×C4 |
| Fitting | M16×C523 | C2 |
| prime radical | #22552641 | C2 |
| cosocle | C4×C523 | C23 |
| hypercenter | M16 | D523 |
| hypocenter | C523 | #131 |
| LCS | G ▷ C2×C523 ▷ C523 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8368 |
Polycyclic presentation:
2^5,523|a^2=d,d^2=e,f^a=f^522,c^b=ce,f^c=f^5222630 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #45690319, #45690321, #45690324, … |
| maximal normal subgroup of | #45690319, #45690321, #45690324, … |
| maximal quotient of | #45690162, #45690163, #45690170, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16736, 154);