Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C8×C131 ⋊ C2 |
| Sylow | C131 ⋊ #443 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D524 |
| commutator | C4×C131 | C22×C4 |
| Frattini | C2×C4 | C22×D131 |
| Fitting | C4×C8×C131 | C2 |
| socle | C2×C131 | C4×D4 |
| hypercenter | C4×C8 | D131 |
| hypocenter | C131 | #443 |
| LCS | G ▷ C4×C131 ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ C4×C8 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=e,c^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^130,d^b=df,g^b=g^1302108 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30663933, #30663935, #30663936, … |
| maximal normal subgroup of | #30663933, #30663935, #30663936, … |
| maximal quotient of | C8×D1048, C8×#14523502, C8×Dic524, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 667);