Finite Group DatabasebetaFinite Group Databasebeta| order | 736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C23 ⋊ C4⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D23 |
| commutator, socle, prime radical, cosocle | C22×C23 | C23 |
| Fitting | C2×Q8×C23 | C2 |
| hypercenter | C2×Q8 | D23 |
| hypocenter | C23 | C4⋊Q8 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^5,23|a^2=e,b^2=d,c^2=d,c^a=ce,f^a=f^22,c^b=cd124 conjugacy classes — view the full character table.
| maximal subgroup of | #13092215, #13092598, #13092600, … |
| maximal normal subgroup of | #13092215, #13092598, #13092600, … |
| maximal quotient of | #13092286, #13092312, #13092322, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(736, 139);