Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C131 ⋊ #395 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D131 |
| commutator, socle | C23×C131 | C23 |
| Fitting | C22×Q8×C131 | C2 |
| hypercenter | C22×Q8 | D131 |
| hypocenter | C131 | #395 |
| LCS | G ▷ C23×C131 ▷ C131 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
182 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,131|a^2=d,b^2=d,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^1301322 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30664921, #30664923, #30664928, … |
| maximal normal subgroup of | #30664921, #30664923, #30664928, … |
| maximal quotient of | #30664211, #30664224, #30664232, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 468);