Finite Group Databasebeta

#46803516

order34208
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC1069 ⋊ #104

Subgroups

subgroupG/H
centerC4C22⋊D1069
commutatorC4×C1069C2×C4
FrattiniC2×C4C2×D1069
Fitting, prime radical#41×C1069C2
socleC2×C1069C22⋊C4
cosocleC2×C4×C1069C22
hypercenter#41D1069
hypocenterC1069#104
LCSG ▷ C4×C1069 ▷ C2×C1069 ▷ C1069
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8552

Polycyclic presentation:

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

Conjugacy classes & character table

5354 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34208, 73);