Finite Group Databasebeta

#45683070

order33056
automorphism?
homologyAbelianization (H1) = C2×C8 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowC1033 ⋊ M32

Subgroups

subgroupG/H
center, FrattiniC8C2×D1033
commutator, socleC2×C1033C2×C8
FittingC2×C8×C1033C2
prime radicalC22×C1033C8
cosocleC8×C1033C22
hypercenterC2×C8D1033
hypocenterC1033M32
LCSG ▷ C2×C1033 ▷ C1033
UCSC1 ◁ C8 ◁ C2×C8

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16528

Polycyclic presentation:

2^5,1033|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^1032

Conjugacy classes & character table

8276 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33056, 86);