Finite Group DatabasebetaFinite Group Databasebeta| order | 16736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C523 ⋊ C2 |
| Sylow | C523 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D523 |
| commutator, cosocle | C4×C523 | C23 |
| Frattini | C4 | C22×D523 |
| Fitting | SD16×C523 | C2 |
| socle | C2×C523 | C2×D4 |
| hypercenter | SD16 | D523 |
| hypocenter | C523 | #135 |
| LCS | G ▷ C4×C523 ▷ C2×C523 ▷ C523 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ SD16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8368 |
Polycyclic presentation:
2^5,523|c^2=e,d^2=e,b^a=bd,d^a=de,d^b=de,f^b=f^522,f^c=f^5221841 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #135×D523, C2×#30660394, #45691001, … |
| maximal normal subgroup of | #135×D523, C2×#30660394, #45691001, … |
| maximal quotient of | #45690198, #45690200, #45690240, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16736, 167);