Finite Group Databasebeta

#46800718

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

Aliases

No aliases for this group.

Splittings

SylowC1061 ⋊ #131

Subgroups

subgroupG/H
center, FrattiniC2C22×#16862558
commutator, socleC2×C1061C22×C4
FittingQ8×C1061C4
prime radical#30684117C2
cosocleDic1061C23
hypercenterQ8#16862558
hypocenterC1061#131
LCSG ▷ C2×C1061 ▷ C1061
UCSC1 ◁ C2 ◁ Q8

62 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16976

Polycyclic presentation:

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

Conjugacy classes & character table

1345 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33952, 234);