Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C23×C22⋊Q8 ⋊ C2 |
| Sylow | C23 ⋊ #542 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D23 |
| commutator, socle, cosocle | C22×C23 | C24 |
| Fitting | C23×C22⋊Q8 | C2 |
| prime radical | #10625055 | C2 |
| hypercenter | C22⋊Q8 | D23 |
| hypocenter | C23 | #542 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 736 |
Polycyclic presentation:
2^6,23|b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,c^b=ce,g^b=g^22,g^c=g^22,g^d=g^22176 conjugacy classes — view the full character table.
| maximal subgroup of | D23×#542, C2×#13093037, #15686780, … |
| maximal normal subgroup of | D23×#542, C2×#13093037, #15686780, … |
| maximal quotient of | #15676003, #15676039, #15676046, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1169);