Finite Group Databasebeta

#46801151

order34016
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

SylowC1063 ⋊ #117

Subgroups

subgroupG/H
center, FrattiniC22C22×D1063
commutatorC2×C1063C22×C4
FittingC22⋊C4×C1063C2
socle, cosocleC22×C1063C23
prime radicalC23×C1063C22
hypercenterC22⋊C4D1063
hypocenterC1063#117
LCSG ▷ C2×C1063 ▷ C1063
UCSC1 ◁ C22 ◁ C22⋊C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17008

Polycyclic presentation:

2^5,1063|a^2=e,c^2=d,b^a=bd,f^c=f^1062

Conjugacy classes & character table

5330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34016, 102);