Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C13×M128 ⋊ C2 |
| Sylow | C13 ⋊ #13742 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D416 |
| commutator, cosocle | C13×C32 | C23 |
| Frattini | C32 | C22×D13 |
| Fitting | C13×M128 | C2 |
| socle | C2×C13 | C2×D32 |
| hypercenter | M128 | D13 |
| hypocenter | C13 | #13742 |
| LCS | G ▷ C13×C32 ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ M128 | |
134 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 832 |
Polycyclic presentation:
2^8,13|d^2=ef,e^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ch,d^a=de,e^a=ef,f^a=fg,g^a=gh,i^a=i^12,d^b=de,e^b=ef,f^b=fg,g^b=gh,i^b=i^12526 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 90628);