Finite Group DatabasebetaFinite Group Databasebeta| order | 11744 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C367 ⋊ C2 |
| Sylow | C367 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D367 |
| commutator, cosocle | C4×C367 | C23 |
| Frattini | C4 | C22×D367 |
| Fitting | SD16×C367 | C2 |
| socle | C2×C367 | C2×D4 |
| hypercenter | SD16 | D367 |
| hypocenter | C367 | #135 |
| LCS | G ▷ C4×C367 ▷ C2×C367 ▷ C367 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ SD16 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,367|c^2=e,d^2=e,b^a=bd,d^a=de,d^b=de,f^b=f^366,f^c=f^3661295 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #135×D367, C2×#26044282, #37554982, … |
| maximal normal subgroup of | #135×D367, C2×#26044282, #37554982, … |
| maximal quotient of | #37554179, #37554181, #37554221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11744, 167);