Finite Group Databasebeta

#46800541

order33952
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC1061 ⋊ #97

Subgroups

subgroupG/H
center, FrattiniC2×C4C2×D1061
commutatorC2×C1061C42
FittingC42×C1061C2
socle, prime radicalC22×C1061C2×C4
cosocleC2×C4×C1061C22
hypercenterC42D1061
hypocenterC1061#97
LCSG ▷ C2×C1061 ▷ C1061
UCSC1 ◁ C2×C4 ◁ C42

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33952

Polycyclic presentation:

2^5,1061|a^2=c,b^2=d,c^2=e,b^a=be,f^a=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, 57);