Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×C269 ⋊ C4 |
| Sylow | C269 ⋊ #97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#11761640 |
| commutator, socle | C2×C269 | C42 |
| Fitting | C8×C269 | C4 |
| hypercenter | C8 | #11761640 |
| hypocenter | C269 | #97 |
| LCS | G ▷ C2×C269 ▷ C269 | |
| UCS | C1 ◁ C4 ◁ C8 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,269|a^2=c,b^2=d,c^2=e,b^a=be,f^b=f^187,f^d=f^268556 conjugacy classes — view the full character table.
| maximal subgroup of | #31771495, #31771496, C2×#22575507, … |
| maximal normal subgroup of | #31771495, #31771496, C2×#22575507, … |
| maximal quotient of | #31771446, #14524137⋊C8, (C2×#11761640)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 200);