Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C47×#431 ⋊ C2 |
| Sylow | C47 ⋊ #2920 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D47 |
| commutator, socle | C22×C47 | C23×C4 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#431 | C2 |
| hypercenter | #431 | D47 |
| hypocenter | C47 | #2920 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C42 ◁ #431 | |
484 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,47|a^2=f,c^2=e,f^2=g,b^a=be,d^a=dg,h^d=h^46976 conjugacy classes — view the full character table.
| maximal subgroup of | #26105678, #26105681, #26105684, … |
| maximal normal subgroup of | #26105678, #26105681, #26105684, … |
| maximal quotient of | #26213750, C4×#15689085, C4×#15689145, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 13138);