Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C131 ⋊ #431 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×D131 |
| commutator | C2×C131 | C22×C8 |
| Frattini | C2×C4 | C22×D131 |
| Fitting | C2×C42×C131 | C2 |
| socle | C22×C131 | C22×C4 |
| hypercenter | C2×C42 | D131 |
| hypocenter | C131 | #431 |
| LCS | G ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C42 ◁ C2×C42 | |
118 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=e,c^2=d,e^2=f,b^a=bd,g^a=g^1302120 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30663789, #30663790, #30663791, … |
| maximal normal subgroup of | #30663789, #30663790, #30663791, … |
| maximal quotient of | #30665707, C4×C22⋊(C131⋊C8), C4×C4⋊(C131⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 602);