Finite Group DatabasebetaFinite Group Databasebeta| order | 8144 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C509 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D509 |
| commutator, socle | C2×C509 | C2×C4 |
| Fitting | C2×C4×C509 | C2 |
| hypercenter | C2×C4 | D509 |
| hypocenter | C509 | M16 |
| LCS | G ▷ C2×C509 ▷ C509 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,509|a^2=c,c^2=d,b^a=bd,e^a=e^5082042 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30654131, #30654132, #30654133, … |
| maximal normal subgroup of | #30654131, #30654132, #30654133, … |
| maximal quotient of | #30654126, C22⋊#16861325, C4⋊#16861325, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8144, 24);