Finite Group Databasebeta

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C5×Dic3×C13×C41 #44544284

order31980
automorphism?
homologyAbelianization (H1) = C4×C5×C13×C41 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic3×C13×C41
unambiguous semidirect productC3⋊(C4×C5×C13×C41)

Splittings

derived, SylowC3 ⋊ C4×C5×C13×C41
HallC3×C5×C13×C41 ⋊ C4
HallC3×C13×C41 ⋊ C4×C5
HallC3×C5×C41 ⋊ C4×C13
HallC3×C5×C13 ⋊ C4×C41
HallC3×C41 ⋊ C4×C5×C13
HallC3×C13 ⋊ C4×C5×C41
HallC3×C5 ⋊ C4×C13×C41

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13×C41D3
commutator, hypocenterC3C4×C5×C13×C41
FrattiniC2C5×D3×C13×C41
Fitting, socle, prime radicalC2×C3×C5×C13×C41C2
cosocleC2×C3C2×C5×C13×C41
LCSG ▷ C3
UCSC1 ◁ C2×C5×C13×C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31980

Conjugacy classes & character table

15990 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 12);