Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C23×2−1+4 ⋊ C2 |
| Sylow | C23 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D23 |
| commutator, socle, cosocle | C2×C23 | C25 |
| Fitting | C23×2−1+4 | C2 |
| hypercenter | 2−1+4 | D23 |
| hypocenter | C23 | #585 |
| LCS | G ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
810 conjugacy classes of subgroups.
| transitive degree | μt(G) = 368 |
Polycyclic presentation:
2^6,23|e^2=f,b^a=bf,d^a=df,c^b=cf,g^c=g^22,g^d=g^22,g^e=g^22221 conjugacy classes — view the full character table.
| maximal subgroup of | #15682744, #15682749, #15682767, … |
| maximal normal subgroup of | #15682744, #15682749, #15682767, … |
| maximal quotient of | #15686597, #15686599, #15686603, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1386);