Finite Group DatabasebetaFinite Group Databasebeta| order | 736 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C23 ⋊ #97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×D23 |
| commutator | C2×C23 | C42 |
| Fitting | C42×C23 | C2 |
| socle, prime radical | C22×C23 | C2×C4 |
| cosocle | C2×C4×C23 | C22 |
| hypercenter | C42 | D23 |
| hypocenter | C23 | #97 |
| LCS | G ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^5,23|a^2=c,b^2=d,c^2=e,b^a=be,f^a=f^22196 conjugacy classes — view the full character table.
| maximal subgroup of | #13092156, #13092157, #13092158, … |
| maximal normal subgroup of | #13092156, #13092157, #13092158, … |
| maximal quotient of | #13092139, #13092172, #13092195, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(736, 9);