Finite Group DatabasebetaFinite Group Databasebeta| order | 10544 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C659 ⋊ C2 |
| Sylow | C659 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D659 |
| commutator, socle, cosocle | C2×C659 | C23 |
| Fitting | Q8×C659 | C2 |
| hypercenter | Q8 | D659 |
| hypocenter | C659 | #41 |
| LCS | G ▷ C2×C659 ▷ C659 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,659|c^2=d,b^a=bd,e^a=e^658,e^b=e^658,e^c=e^6581655 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35231340, #35231342, #35231346, … |
| maximal normal subgroup of | #35231340, #35231342, #35231346, … |
| maximal quotient of | #35231277, #35231281, Q8×Dic659, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10544, 41);