Finite Group DatabasebetaFinite Group Databasebeta| order | 6016 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C47 ⋊ #2351 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator | C22×C47 | C23×C4 |
| Fitting | C2×C4×Q8×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C2×C4×Q8 | D47 |
| hypocenter | C47 | #2351 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C2×C4×Q8 | |
552 conjugacy classes of subgroups; only the 313 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 313 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,47|a^2=g,b^2=e,c^2=ef,d^2=e,b^a=be,c^a=cf,h^a=h^46,d^b=de970 conjugacy classes — view the full character table.
| maximal subgroup of | #26109851, #26109855, #26109856, … |
| maximal normal subgroup of | #26109851, #26109855, #26109856, … |
| maximal quotient of | #26137724, Q8×C47⋊#95, #26137851, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6016, 7431);