Finite Group DatabasebetaFinite Group Databasebeta| order | 3008 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #135×C47 ⋊ C2 |
| Sylow | C47 ⋊ #577 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D4×D47 |
| commutator, cosocle | C4×C47 | C24 |
| Frattini | C4 | C23×D47 |
| Fitting | #135×C47 | C2 |
| socle | C2×C47 | C22×D4 |
| hypercenter | #135 | D47 |
| hypocenter | C47 | #577 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #135 | |
258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 752 |
Polycyclic presentation:
2^6,47|a^2=f,e^2=f,b^a=be,e^a=ef,e^b=ef,d^c=df,g^c=g^46,g^d=g^46344 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3008, 1356);