Finite Group DatabasebetaFinite Group Databasebeta| order | 11744 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×Dic367 |
| Sylow | C367 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D367 |
| commutator | C2×C367 | C22×C4 |
| Fitting, prime radical | C2×D4×C367 | C2 |
| socle, cosocle | C22×C367 | C23 |
| hypercenter | C2×D4 | D367 |
| hypocenter | C367 | C4×D4 |
| LCS | G ▷ C2×C367 ▷ C367 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
94 conjugacy classes of subgroups.
1850 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #37554266, D8×Dic367, SD16×Dic367, … |
| maximal normal subgroup of | #37554266, D8×Dic367, SD16×Dic367, … |
| maximal quotient of | C22⋊C4×Dic367, C4⋊C4×Dic367, #37554061, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11744, 109);