Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Sylow | C32 ⋊ C2×#379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D32 |
| commutator | C22×C32 | C23×C4 |
| Fitting | C25×C32 | C22 |
| socle, cosocle | C23×C32 | C24 |
| prime radical | C25×C3⋊D3 | C2 |
| hypercenter | C25 | D32 |
| hypocenter | C32 | C2×#379 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ C25 | |
9753 conjugacy classes of subgroups; only the 484 normal subgroups are shown.
This group has 9753 conjugacy classes of subgroups — too many to draw. Only its 484 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:
2^7,3^2|a^2=g,b^a=be,c^a=cf,i^a=hi^2,h^d=h^2,i^d=i^2144 conjugacy classes — view the full character table.
| maximal subgroup of | #72214860, #72252255, #72252263, … |
| maximal normal subgroup of | #72214860, #72252255, #72252263, … |
| maximal quotient of | #72214791, #72252282, #72252283 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 34976);