Finite Group DatabasebetaFinite Group Databasebeta| order | 8656 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C541 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#14524194 |
| commutator, socle | C2×C541 | C2×C4 |
| Fitting | C22×C541 | C4 |
| hypercenter | C22 | #14524194 |
| hypocenter | C541 | M16 |
| LCS | G ▷ C2×C541 ▷ C541 | |
| UCS | C1 ◁ C2 ◁ C22 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,541|a^2=c,c^2=d,b^a=bd,e^a=e^52,e^c=e^540550 conjugacy classes — view the full character table.
| maximal subgroup of | #31772688, #31772689, C2×#22575845, … |
| maximal normal subgroup of | #31772688, #31772689, C2×#22575845, … |
| maximal quotient of | #31772683, C22⋊#16864520, #31772695, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8656, 49);