Finite Group Databasebeta

#46800570

order33952
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC1061 ⋊ M32

Subgroups

subgroupG/H
center, FrattiniC8C2×D1061
commutator, socleC2×C1061C2×C8
FittingC2×C8×C1061C2
prime radicalC22×C1061C8
cosocleC8×C1061C22
hypercenterC2×C8D1061
hypocenterC1061M32
LCSG ▷ C2×C1061 ▷ C1061
UCSC1 ◁ C8 ◁ C2×C8

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16976

Polycyclic presentation:

2^5,1061|a^2=c,c^2=d,d^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, 86);