Finite Group Databasebeta

#45683057

order33056
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC1033 ⋊ #104

Subgroups

subgroupG/H
centerC4C22⋊D1033
commutatorC4×C1033C2×C4
FrattiniC2×C4C2×D1033
Fitting, prime radical#41×C1033C2
socleC2×C1033C22⋊C4
cosocleC2×C4×C1033C22
hypercenter#41D1033
hypocenterC1033#104
LCSG ▷ C4×C1033 ▷ C2×C1033 ▷ C1033
UCSC1 ◁ C4 ◁ C2×C4 ◁ #41

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8264

Polycyclic presentation:

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

Conjugacy classes & character table

5174 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33056, 73);