Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C131 ⋊ #340 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D524 |
| commutator | C4×C131 | C42 |
| Frattini | C22×C4 | C2×D131 |
| Fitting | C22×C8×C131 | C2 |
| socle | C23×C131 | D4 |
| hypercenter | C22×C8 | D131 |
| hypocenter | C131 | #340 |
| LCS | G ▷ C4×C131 ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ C22×C8 | |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=d,b^2=e,c^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^a=g^1302108 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30663970, #30663971, #30663973, … |
| maximal normal subgroup of | #30663970, #30663971, #30663973, … |
| maximal quotient of | #30663796, #30663801, #30663820, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 312);