Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C139 ⋊ C2 |
| Sylow | C139 ⋊ #394 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D139 |
| commutator, socle | C23×C139 | C23 |
| Fitting | C2×C22⋊C4×C139 | C2 |
| hypercenter | C2×C22⋊C4 | D139 |
| hypocenter | C139 | #394 |
| LCS | G ▷ C23×C139 ▷ C139 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,139|c^2=d,b^a=bd,c^a=ce,c^b=cf,g^b=g^138,g^c=g^1381402 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #394×D139, C2×#22580869, #31809616, … |
| maximal normal subgroup of | #394×D139, C2×#22580869, #31809616, … |
| maximal quotient of | #31804643, #31804649, #31804650, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 465);