Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×Q8×C137 ⋊ C4 |
| Sylow | C137 ⋊ #519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#10587739 |
| commutator, socle | C2×C137 | C23×C4 |
| Fitting | C2×Q8×C137 | C4 |
| hypercenter | C2×Q8 | #10587739 |
| hypocenter | C137 | #519 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
266 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=f,b^2=e,c^2=e,b^a=be,d^a=de,g^a=g^100,c^b=ce,g^f=g^136374 conjugacy classes — view the full character table.
| maximal subgroup of | #31796745, #31796795, #31796797, … |
| maximal normal subgroup of | #31796745, #31796795, #31796797, … |
| maximal quotient of | #31797227, #31797229, #31797263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1617);