Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Sylow | C32 ⋊ #394 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×C3⋊D3 |
| commutator, socle, cosocle | C23×C32 | C23 |
| Fitting, prime radical | C22×C32×D4 | C2 |
| hypercenter | C22×D4 | C3⋊D3 |
| hypocenter | C32 | #394 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
714 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^6,3^2|a^2=f,b^a=be,c^a=cd,g^a=g^2,h^a=h^2,c^b=cf102 conjugacy classes — view the full character table.
| maximal subgroup of | #11771822, #11778042, #11778048, … |
| maximal normal subgroup of | #11771822, #11778042, #11778048, … |
| maximal quotient of | #11773278, #11773294, #11773326, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 4803);