Finite Group DatabasebetaFinite Group Databasebeta| order | 18176 |
| automorphism | ? |
| homology | Abelianization (H1) = C27 · Schur multiplier (H2) = C220 |
No aliases for this group.
| Fitting | C71×2−1+6 ⋊ C2 |
| Sylow | C71 ⋊ #63103 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C26×D71 |
| commutator, socle, cosocle | C2×C71 | C27 |
| Fitting | C71×2−1+6 | C2 |
| hypercenter | 2−1+6 | D71 |
| hypocenter | C71 | #63103 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C2 ◁ 2−1+6 | |
59452 conjugacy classes of subgroups; only the 32039 normal subgroups are shown.
This group has 59452 conjugacy classes of subgroups — too many to draw. Only its 32039 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2272 |
Polycyclic presentation:
2^8,71|g^2=h,b^a=bh,f^a=fh,e^b=eh,d^c=dh,i^e=i^70,i^f=i^70,i^g=i^702405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18176, 1083471);