Finite Group DatabasebetaFinite Group Databasebeta| order | 13712 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×#16812170 |
| Fitting | C4×C857 ⋊ C4 |
| derived, Sylow | C857 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #16812170 |
| commutator, hypocenter | C857 | C42 |
| Frattini | C2 | C2×#16812170 |
| Fitting | C4×C857 | C4 |
| socle | C2×C857 | C2×C4 |
| prime radical, cosocle | C2×D857 | C22 |
| LCS | G ▷ C857 | |
| UCS | C1 ◁ C4 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3428 |
872 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#16812170, #42116883, #42116893, … |
| maximal normal subgroup of | C8×#16812170, #42116883, #42116893, … |
| maximal quotient of | (C2×#16812170)⋊C4, C8×#16812170, C4×#20293514, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13712, 44);