Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C3 |
| direct product | Q8×#622 |
| Sylow | C32 ⋊ C8×Q8 |
172 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
60 conjugacy classes — view the full character table.
| maximal subgroup of | Q8⋊#3771, #11777185, SD16×#622, … |
| maximal normal subgroup of | Q8⋊#3771, #11777185, SD16×#622, … |
| maximal quotient of | C4⋊C4×#622, #11788954, #11790031, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5715);