Finite Group DatabasebetaFinite Group Databasebeta| order | 11344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C709 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#15667778 |
| commutator, socle | C2×C709 | C2×C4 |
| Fitting | C4×C709 | C4 |
| prime radical | C2×D709 | C4 |
| cosocle | Dic709 | C22 |
| hypercenter | C4 | #15667778 |
| hypocenter | C709 | M16 |
| LCS | G ▷ C2×C709 ▷ C709 | |
| UCS | C1 ◁ C2 ◁ C4 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,709|a^2=c,c^2=d,b^a=bd,e^a=e^96,e^b=e^708,e^c=e^708718 conjugacy classes — view the full character table.
| maximal subgroup of | #36383967, #36383968, #36383973, … |
| maximal normal subgroup of | #36383967, #36383968, #36383973, … |
| maximal quotient of | #36383958, #36383960, C4⋊#19150893, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11344, 50);