Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(7,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C137 · Schur multiplier (H2) = C214 |
| direct product | H(7,𝔽2)×C137 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C137 | C26 |
| commutator, Frattini, cosocle | C2 | C26×C137 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C137 ◁ G | |
5992 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2192 |
8905 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C137×#32894, C137×#32896 |
| maximal normal subgroup of | C137×#32894, C137×#32896 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 2326);