Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C23×H(5,𝔽2) ⋊ C2 |
| Sylow | C23 ⋊ #585 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D23 |
| commutator, socle, cosocle | C2×C23 | C25 |
| Fitting | C23×H(5,𝔽2) | C2 |
| hypercenter | H(5,𝔽2) | D23 |
| hypocenter | C23 | #585 |
| LCS | G ▷ C2×C23 ▷ C23 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
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^e=g^22221 conjugacy classes — view the full character table.
| maximal subgroup of | #15682742, #15682747, #15682765, … |
| maximal normal subgroup of | #15682742, #15682747, #15682765, … |
| maximal quotient of | #15686595, #15686597, #15686601, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1384);