Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×M16×C23 ⋊ C2 |
| Sylow | C23 ⋊ #568 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D23 |
| commutator, socle | C2×C23 | C23×C4 |
| Fitting | C2×M16×C23 | C2 |
| prime radical | C2×#67288 | C2 |
| cosocle | C4×C23 | C24 |
| hypercenter | C2×M16 | D23 |
| hypocenter | C23 | #568 |
| LCS | G ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C4 ◁ C2×M16 | |
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 368 |
Polycyclic presentation:
2^6,23|a^2=e,e^2=f,d^a=df,c^b=cf,g^c=g^22254 conjugacy classes — view the full character table.
| maximal subgroup of | #15673615, #15673618, #15673634, … |
| maximal normal subgroup of | #15673615, #15673618, #15673634, … |
| maximal quotient of | #15681814, #15681815, #15681822, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1315);