Finite Group Databasebeta

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C3×#24922523 #44544408

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

Aliases

direct productC3×#24922523

Splittings

Fitting, socle, HallC3×C5×C13×C41 ⋊ C4
derived, HallC5×C13×C41 ⋊ C3×C4
HallC3×C13×C41 ⋊ AGL(1,𝔽5)
HallC3×C5×C41 ⋊ #261
HallC13×C41 ⋊ C3×AGL(1,𝔽5)
HallC5×C41 ⋊ C3×#261
HallC3×C5×C13 ⋊ #4223
HallC3×C41 ⋊ #63121
HallC5×C13 ⋊ C3×#4223
SylowC41 ⋊ C3×#63121
HallC3×C13 ⋊ #11717961
HallC3×C5 ⋊ #14523822
SylowC13 ⋊ C3×#11717961
SylowC5 ⋊ C3×#14523822

Subgroups

subgroupG/H
center, hypercenterC3#24922523
commutator, hypocenterC5×C13×C41C3×C4
FrattiniC1G
Fitting, socleC3×C5×C13×C41C4
prime radicalC3×D2665C2
cosocleD2665C2×C3
LCSG ▷ C5×C13×C41
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7995

Conjugacy classes & character table

2010 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 136);