Finite Group DatabasebetaFinite Group Databasebeta| order | 11344 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C709 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D709 |
| commutator | C2×C709 | C2×C4 |
| Fitting | C2×C4×C709 | C2 |
| socle, prime radical, cosocle | C22×C709 | C22 |
| hypercenter | C2×C4 | D709 |
| hypocenter | C709 | C4⋊C4 |
| LCS | G ▷ C2×C709 ▷ C709 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,709|a^2=d,b^2=c,b^a=bc,e^b=e^7082842 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4⋊C4×D709, C2×#26015372, #36383859, … |
| maximal normal subgroup of | C4⋊C4×D709, C2×#26015372, #36383859, … |
| maximal quotient of | #36383810, #36383832, #36383834, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11344, 19);