Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | C3×SL(2,𝔽3) ⋊ C2×C4 |
169 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 169 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^3,3^2,2^3|a^2=h,b^2=c,f^2=h,g^2=h,b^a=bh,e^a=e^2,d^b=d^2,f^b=gh,g^b=fh,f^d=g,g^d=fgh,g^f=gh42 conjugacy classes — view the full character table.
| maximal subgroup of | #11921480, #11921482, #11921492, … |
| maximal normal subgroup of | #11921480, #11921482, #11921492, … |
| maximal quotient of | #11920499, #11920500, #11920658, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 5082);