Finite Group DatabasebetaFinite Group Databasebeta| order | 736 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C23 ⋊ C2 |
| Sylow | C23 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D23 |
| commutator, socle | C2×C23 | C22×C4 |
| Fitting | M16×C23 | C2 |
| prime radical | #67288 | C2 |
| cosocle | C4×C23 | C23 |
| hypercenter | M16 | D23 |
| hypocenter | C23 | #131 |
| LCS | G ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C4 ◁ M16 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 368 |
Polycyclic presentation:
2^5,23|c^2=d,d^2=e,b^a=be,f^a=f^22,c^b=ce130 conjugacy classes — view the full character table.
| maximal subgroup of | #13092531, #13092533, #13092536, … |
| maximal normal subgroup of | #13092531, #13092533, #13092536, … |
| maximal quotient of | #13092374, #13092375, #13092382, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(736, 102);