Finite Group DatabasebetaFinite Group Databasebeta| order | 8576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16863354 |
| Sylow | C67 ⋊ C2×#405 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D67 |
| commutator | C2×C67 | C22×C42 |
| Frattini | C2×C4 | C23×D67 |
| Fitting | C22×M16×C67 | C2 |
| socle | C23×C67 | C22×C4 |
| hypercenter | C22×M16 | D67 |
| hypocenter | C67 | C2×#405 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C22×C4 ◁ C22×M16 | |
592 conjugacy classes of subgroups.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30760999, #30761001, #30761022, … |
| maximal normal subgroup of | #30760999, #30761001, #30761022, … |
| maximal quotient of | C2×M16×C67⋊C8, C2×#22558493, C2×#22558496, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8576, 12925);