Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×Q8×C3⋊Dic3 |
| Sylow | C32 ⋊ C2×C4×Q8 |
894 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #11773833, #11773968, C2×Q8⋊#622, … |
| maximal normal subgroup of | #11773833, #11773968, C2×Q8⋊#622, … |
| maximal quotient of | C2×C4⋊C4×C3⋊Dic3, C4×Q8×C3⋊Dic3, C2×#10592679, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 8164);