Finite Group DatabasebetaFinite Group Databasebeta| order | 11008 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C43×#3458 ⋊ C2 |
| Sylow | C43 ⋊ #62686 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C24×D43 |
| commutator, socle, cosocle | C22×C43 | C26 |
| Frattini | C22 | C25×D43 |
| Fitting | C43×#3458 | C2 |
| hypercenter | #3458 | D43 |
| hypocenter | C43 | #62686 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ #3458 | |
7226 conjugacy classes of subgroups.
Polycyclic presentation:
2^8,43|e^2=h,f^2=g,b^a=bg,c^a=ch,d^a=dh,i^a=i^42,c^b=ch,i^b=i^42,i^f=i^421012 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11008, 1076432);