Finite Group DatabasebetaFinite Group Databasebeta| order | 17984 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C281 ⋊ C4×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D281 |
| commutator | C2×C281 | C2×C42 |
| Fitting | #95×C281 | C2 |
| socle, prime radical, cosocle | C23×C281 | C23 |
| hypercenter | #95 | D281 |
| hypocenter | C281 | C4×C4⋊C4 |
| LCS | G ▷ C2×C281 ▷ C281 | |
| UCS | C1 ◁ C23 ◁ #95 | |
194 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17984 |
Polycyclic presentation:
2^6,281|a^2=e,b^2=f,c^2=de,b^a=bd,g^c=g^2802840 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49093796, #49093800, #49093825, … |
| maximal normal subgroup of | #49093796, #49093800, #49093825, … |
| maximal quotient of | #95×Dic281, #49093527, #49093531, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17984, 400);