Finite Group Databasebeta

#45685124

order33248
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

No aliases for this group.

Splittings

SylowC1039 ⋊ #100

Subgroups

subgroupG/H
centerC2C22⋊Dic1039
commutatorC22×C1039C2×C4
FrattiniC2×C4C2×D1039
Fitting, prime radicalC2×D4×C1039C2
socleC2×C1039C22⋊C4
cosocleC2×C4×C1039C22
hypercenterC2×D4D1039
hypocenterC1039#100
LCSG ▷ C22×C1039 ▷ C2×C1039 ▷ C1039
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

46 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8312

Polycyclic presentation:

2^5,1039|a^2=d,d^2=e,b^a=bc,c^a=ce,f^a=f^1038,d^b=de

Conjugacy classes & character table

5201 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33248, 63);