Finite Group Databasebeta

#46803496

order34208
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C23

Aliases

No aliases for this group.

Splittings

SylowC1069 ⋊ #95

Subgroups

subgroupG/H
center, FrattiniC23C2×D1069
commutatorC2×C1069C42
FittingC22×C4×C1069C2
socle, prime radical, cosocleC23×C1069C22
hypercenterC22×C4D1069
hypocenterC1069#95
LCSG ▷ C2×C1069 ▷ C1069
UCSC1 ◁ C23 ◁ C22×C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34208

Polycyclic presentation:

2^5,1069|a^2=d,b^2=e,b^a=bc,f^b=f^1068

Conjugacy classes & character table

8564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34208, 53);