Finite Group Databasebeta

#45683037

order33056
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C23

Aliases

No aliases for this group.

Splittings

SylowC1033 ⋊ #95

Subgroups

subgroupG/H
center, FrattiniC23C2×D1033
commutatorC2×C1033C42
FittingC22×C4×C1033C2
socle, prime radical, cosocleC23×C1033C22
hypercenterC22×C4D1033
hypocenterC1033#95
LCSG ▷ C2×C1033 ▷ C1033
UCSC1 ◁ C23 ◁ C22×C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33056

Polycyclic presentation:

2^5,1033|a^2=d,b^2=e,b^a=bc,f^b=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, 53);