Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C137 ⋊ #395 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D137 |
| commutator, socle | C23×C137 | C23 |
| Fitting | C22×Q8×C137 | C2 |
| hypercenter | C22×Q8 | D137 |
| hypocenter | C137 | #395 |
| LCS | G ▷ C23×C137 ▷ C137 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
182 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=d,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^1361382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31779749, #31779751, #31779756, … |
| maximal normal subgroup of | #31779749, #31779751, #31779756, … |
| maximal quotient of | #31779039, #31779052, #31779060, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 468);