Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C127 ⋊ C4×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D127 |
| commutator | C2×C127 | C2×C42 |
| Fitting | #95×C127 | C2 |
| socle | C23×C127 | C23 |
| hypercenter | #95 | D127 |
| hypocenter | C127 | C4×C4⋊C4 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C23 ◁ #95 | |
194 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=e,b^2=f,c^2=de,b^a=bd,g^c=g^1261300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30637223, #30637227, #30637252, … |
| maximal normal subgroup of | #30637223, #30637227, #30637252, … |
| maximal quotient of | #95×Dic127, #30636954, Dic127⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 400);