Finite Group DatabasebetaFinite Group Databasebeta| order | 3104 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C97 ⋊ C2 |
| Sylow | C97 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | D388 |
| commutator, cosocle | C4×C97 | C23 |
| Frattini | C4 | C22×D97 |
| Fitting | C2×C8×C97 | C2 |
| socle | C2×C97 | C2×D4 |
| hypercenter | C2×C8 | D97 |
| hypocenter | C97 | #135 |
| LCS | G ▷ C4×C97 ▷ C2×C97 ▷ C97 | |
| UCS | C1 ◁ C4 ◁ C2×C4 ◁ C2×C8 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1552 |
Polycyclic presentation:
2^5,97|c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^96,d^b=de,f^b=f^96782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3104, 168);