Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C4×D4×C67 ⋊ C2 |
| Sylow | C67 ⋊ #2630 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D67 |
| commutator, socle | C23×C67 | C24 |
| Fitting | C2×C4×D4×C67 | C2 |
| hypercenter | C2×C4×D4 | D67 |
| hypocenter | C67 | #2630 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 | |
562 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,67|d^2=f,b^a=be,c^a=cf,c^b=cg,d^c=de,h^c=h^661352 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2630×D67, C2×#22566046, #31022248, … |
| maximal normal subgroup of | #2630×D67, C2×#22566046, #31022248, … |
| maximal quotient of | #30782285, #30782300, #30782315, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 10347);