Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #97×C127 ⋊ C2 |
| Sylow | C127 ⋊ C4×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D127 |
| commutator | C2×C127 | C2×C42 |
| Fitting | #97×C127 | C2 |
| socle | C22×C127 | C22×C4 |
| hypercenter | #97 | D127 |
| hypocenter | C127 | C4×M16 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C2×C4 ◁ #97 | |
142 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=d,b^2=e,d^2=f,c^a=cf,g^b=g^126,g^c=g^1261300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30637315, #30637317, #30637320, … |
| maximal normal subgroup of | #30637315, #30637317, #30637320, … |
| maximal quotient of | #30637009, #30637018, #30637026, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 501);