Finite Group DatabasebetaFinite Group Databasebeta| order | 8656 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4×C541 ⋊ C2 |
| Sylow | C541 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D541 |
| commutator, socle | C2×C541 | C23 |
| Fitting | D4×C541 | C2 |
| hypercenter | D4 | D541 |
| hypocenter | C541 | #41 |
| LCS | G ▷ C2×C541 ▷ C541 | |
| UCS | C1 ◁ C2 ◁ D4 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,541|c^2=d,b^a=bd,e^c=e^5401360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31772647, #31772649, #31772652, … |
| maximal normal subgroup of | #31772647, #31772649, #31772652, … |
| maximal quotient of | #31772584, #31772586, #31772588, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8656, 39);