Finite Group Databasebeta

#46800587

order33952
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4

Aliases

No aliases for this group.

Splittings

FittingC42×C1061 ⋊ C2
SylowC1061 ⋊ #117

Subgroups

subgroupG/H
centerC2×C4C2×D1061
commutatorC2×C1061C22×C4
FrattiniC22C22×D1061
FittingC42×C1061C2
socle, cosocleC22×C1061C23
prime radicalC22×D1061C22
hypercenterC42D1061
hypocenterC1061#117
LCSG ▷ C2×C1061 ▷ C1061
UCSC1 ◁ C2×C4 ◁ C42

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16976

Polycyclic presentation:

2^5,1061|a^2=e,c^2=d,b^a=bd,f^b=f^1060

Conjugacy classes & character table

8500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33952, 103);