Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C23 ⋊ #383 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D23 |
| commutator | C22×C23 | C22×C4 |
| Fitting | C2×C42×C23 | C2 |
| socle, prime radical, cosocle | C23×C23 | C23 |
| hypercenter | C2×C42 | D23 |
| hypocenter | C23 | #383 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1472 |
Polycyclic presentation:
2^6,23|a^2=f,b^2=de,c^2=d,b^a=bd,c^a=ce,g^a=g^22380 conjugacy classes — view the full character table.
| maximal subgroup of | #15671262, #15671263, #15671944, … |
| maximal normal subgroup of | #15671262, #15671263, #15671944, … |
| maximal quotient of | #15671624, #15671659, #15673540, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 417);