Finite Group Databasebeta

#46800690

order33952
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC1061 ⋊ #100

Subgroups

subgroupG/H
centerC2C22⋊#16862558
commutatorC22×C1061C2×C4
FrattiniC22C2×#16862558
FittingC23×C1061C4
socleC2×C1061C22⋊C4
prime radicalC2×C22⋊D1061C2
cosocleC2×Dic1061C22
hypercenterC23#16862558
hypocenterC1061#100
LCSG ▷ C22×C1061 ▷ C2×C1061 ▷ C1061
UCSC1 ◁ C2 ◁ C22 ◁ C23

46 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8488

Polycyclic presentation:

2^5,1061|a^2=d,d^2=e,b^a=bc,c^a=ce,f^a=f^958,d^b=de,f^d=f^1060

Conjugacy classes & character table

2131 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33952, 206);