Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×D4×C23 ⋊ C2 |
| Sylow | C23 ⋊ #525 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D23 |
| commutator, socle, cosocle | C22×C23 | C24 |
| Frattini | C22 | C23×D23 |
| Fitting | C4×D4×C23 | C2 |
| hypercenter | C4×D4 | D23 |
| hypocenter | C23 | #525 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 368 |
Polycyclic presentation:
2^6,23|d^2=e,b^a=be,c^a=cf,g^b=g^22248 conjugacy classes — view the full character table.
| maximal subgroup of | #15682086, #15682088, #15682095, … |
| maximal normal subgroup of | #15682086, #15682088, #15682095, … |
| maximal quotient of | #15675778, #15675836, #15675838, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1058);