Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×#14556313 |
| Fitting | C8×C577 ⋊ C4 |
| derived, Sylow | C577 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #14556313 |
| commutator, hypocenter | C577 | C4×C8 |
| Frattini | C4 | C2×#14556313 |
| Fitting | C8×C577 | C4 |
| socle | C2×C577 | C42 |
| prime radical | C2×D577 | C2×C4 |
| cosocle | C4×D577 | C22 |
| LCS | G ▷ C577 | |
| UCS | C1 ◁ C8 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4616 |
1184 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×#14556313, #49148836, C2×C8×#14556313, … |
| maximal normal subgroup of | C16×#14556313, #49148836, C2×C8×#14556313, … |
| maximal quotient of | C8×#17987237, #49148791, #49148814, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 198);