Finite Group Databasebeta

#46800576

order33952
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC1061 ⋊ Q32

Subgroups

subgroupG/H
centerC2#30684101
commutator, cosocleC8×C1061C22
FrattiniC8C2×D1061
FittingQ16×C1061C2
socle, prime radicalC2×C1061D8
hypercenterQ16D1061
hypocenterC1061Q32
LCSG ▷ C8×C1061 ▷ C4×C1061 ▷ C2×C1061 ▷ C1061
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q16

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33952

Polycyclic presentation:

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

Conjugacy classes & character table

3721 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33952, 92);