Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C137 ⋊ C2 |
| Sylow | C137 ⋊ #405 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×D137 |
| commutator | C2×C137 | C2×C42 |
| Frattini | C2×C4 | C22×D137 |
| Fitting | C4×C8×C137 | C2 |
| socle | C22×C137 | C22×C4 |
| hypercenter | C4×C8 | D137 |
| hypocenter | C137 | #405 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C8 | |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=e,d^2=f,c^b=cf,g^c=g^1362216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31782384, #31782387, #31782546, … |
| maximal normal subgroup of | #31782384, #31782387, #31782546, … |
| maximal quotient of | C8×#14555493, #31779071, #31779077, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 503);