Finite Group DatabasebetaFinite Group Databasebeta| order | 13856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×Dic433 |
| Sylow | C433 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D433 |
| commutator | C2×C433 | C22×C4 |
| Fitting, prime radical | C2×D4×C433 | C2 |
| socle, cosocle | C22×C433 | C23 |
| hypercenter | C2×D4 | D433 |
| hypocenter | C433 | C4×D4 |
| LCS | G ▷ C2×C433 ▷ C433 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6928 |
2180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #42121891, D8×Dic433, SD16×Dic433, … |
| maximal normal subgroup of | #42121891, D8×Dic433, SD16×Dic433, … |
| maximal quotient of | C22⋊C4×Dic433, C4⋊C4×Dic433, #42121686, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13856, 109);