Finite Group DatabasebetaFinite Group Databasebeta| order | 18112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C283 ⋊ #400 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D283 |
| commutator, socle, prime radical, cosocle | C23×C283 | C23 |
| Fitting | C2×C4⋊C4×C283 | C2 |
| hypercenter | C2×C4⋊C4 | D283 |
| hypocenter | C283 | #400 |
| LCS | G ▷ C23×C283 ▷ C283 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18112 |
Polycyclic presentation:
2^6,283|a^2=d,b^2=de,c^2=d,b^a=bd,c^a=ce,c^b=cf,g^b=g^2822842 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49119287, #49119289, #49120292, … |
| maximal normal subgroup of | #49119287, #49119289, #49120292, … |
| maximal quotient of | #49119514, #49119517, #49119520, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18112, 488);