Finite Group Databasebeta

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C3×C13×AGL(1,𝔽5)×C41 #44544399

order31980
automorphism?
homologyAbelianization (H1) = C3×C4×C13×C41 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×AGL(1,𝔽5)×C41

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C4
derived, SylowC5 ⋊ C3×C4×C13×C41
HallC5×C13×C41 ⋊ C3×C4
HallC3×C5×C41 ⋊ C4×C13
HallC5×C41 ⋊ C3×C4×C13
HallC3×C5×C13 ⋊ C4×C41
HallC5×C13 ⋊ C3×C4×C41
HallC3×C5 ⋊ C4×C13×C41

Subgroups

subgroupG/H
center, hypercenterC3×C13×C41AGL(1,𝔽5)
commutator, hypocenterC5C3×C4×C13×C41
FrattiniC1G
Fitting, socleC3×C5×C13×C41C4
prime radicalC3×D5×C13×C41C2
cosocleD5C2×C3×C13×C41
LCSG ▷ C5
UCSC1 ◁ C3×C13×C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

7995 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 127);