Finite Group Databasebeta

#45683095

order33056
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

No aliases for this group.

Splittings

SylowC1033 ⋊ C4×Q8

Subgroups

subgroupG/H
center, FrattiniC22C22×D1033
commutatorC2×C1033C22×C4
FittingC4⋊C4×C1033C2
socle, prime radical, cosocleC22×C1033C23
hypercenterC4⋊C4D1033
hypocenterC1033C4×Q8
LCSG ▷ C2×C1033 ▷ C1033
UCSC1 ◁ C22 ◁ C4⋊C4

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33056

Polycyclic presentation:

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

Conjugacy classes & character table

5180 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33056, 111);