Finite Group DatabasebetaFinite Group Databasebeta| order | 13792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×C431⋊C16 |
| unambiguous semidirect product | (C2×C431)⋊C16 |
| derived, Sylow | C431 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D431 |
| commutator, hypocenter | C431 | C2×C16 |
| Frattini | C8 | C2×D431 |
| Fitting | C2×C8×C431 | C2 |
| socle, prime radical | C22×C431 | C8 |
| cosocle | C8×C431 | C22 |
| LCS | G ▷ C431 | |
| UCS | C1 ◁ C2×C8 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13792 |
3472 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×Dic431, C4×C431⋊C16, #42118834, … |
| maximal normal subgroup of | C16×Dic431, C4×C431⋊C16, #42118834, … |
| maximal quotient of | C4×C431⋊C16, C22⋊(C431⋊C16), C4⋊(C431⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13792, 84);