Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C32 ⋊ C2×#131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D32 |
| commutator, socle | C2×C32 | C23×C4 |
| Fitting | C32×#41 | C22 |
| prime radical | #41×C3⋊D3 | C2 |
| cosocle | C32×C4 | C24 |
| hypercenter | #41 | D32 |
| hypocenter | C32 | C2×#131 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C4 ◁ #41 | |
614 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 194 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3^2|a^2=e,b^2=e,e^2=f,h^a=h^2,g^b=g^2,d^c=df90 conjugacy classes — view the full character table.
| maximal subgroup of | #11787052, #11787411, #11788645, … |
| maximal normal subgroup of | #11787052, #11787411, #11788645, … |
| maximal quotient of | #11857199, #11857278, #11857280, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 7324);