Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8 · Schur multiplier (H2) = C43 |
| direct product | C4×#63553 |
| derived, Sylow | C32 ⋊ C42×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D32 |
| commutator, hypocenter | C32 | C42×C8 |
| Frattini | C22×C4 | C2×D32 |
| Fitting | C2×C32×C42 | C22 |
| socle, prime radical | C23×C32 | C22×C4 |
| cosocle | C22×C32×C4 | C23 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C2×C42 | |
945 conjugacy classes of subgroups; only the 420 normal subgroups are shown.
This group has 945 conjugacy classes of subgroups — too many to draw. Only its 420 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 17025);