Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M16×C277 ⋊ C2 |
| Sylow | C277 ⋊ #100 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #17984540 |
| commutator | C22×C277 | C2×C4 |
| Frattini | C2×C4 | C2×D277 |
| Fitting | M16×C277 | C2 |
| socle | C2×C277 | C22⋊C4 |
| hypercenter | M16 | D277 |
| hypocenter | C277 | #100 |
| LCS | G ▷ C22×C277 ▷ C2×C277 ▷ C277 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ M16 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,277|a^2=d,d^2=e,b^a=bc,c^a=ce,d^b=de,f^b=f^2761391 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #100×D277, C2×#22579796, #31799984, … |
| maximal normal subgroup of | #100×D277, C2×#22579796, #31799984, … |
| maximal quotient of | #31799725, #31799741, #31799745, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 62);