Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#14524137 |
| Sylow | C269 ⋊ C22⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×#11761640 |
| commutator | C2×C269 | C2×C8 |
| Fitting | C23×C269 | C4 |
| socle | C22×C269 | C2×C4 |
| hypercenter | C23 | #11761640 |
| hypocenter | C269 | C22⋊C8 |
| LCS | G ▷ C2×C269 ▷ C269 | |
| UCS | C1 ◁ C22 ◁ C23 | |
50 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,269|a^2=d,d^2=e,b^a=bc,f^a=f^187,f^d=f^268556 conjugacy classes — view the full character table.
| maximal subgroup of | #31771448, #31771449, #31771450, … |
| maximal normal subgroup of | #31771448, #31771449, #31771450, … |
| maximal quotient of | #31771448, #31771450, D4⋊#14524137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 202);