Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C23 ⋊ #395 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D23 |
| commutator, socle, prime radical, cosocle | C23×C23 | C23 |
| Fitting | C22×Q8×C23 | C2 |
| hypercenter | C22×Q8 | D23 |
| hypocenter | C23 | #395 |
| LCS | G ▷ C23×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
182 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1472 |
Polycyclic presentation:
2^6,23|a^2=d,b^2=d,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^22242 conjugacy classes — view the full character table.
| maximal subgroup of | #15672357, #15672359, #15672364, … |
| maximal normal subgroup of | #15672357, #15672359, #15672364, … |
| maximal quotient of | #15671647, #15671660, #15671668, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 468);