Finite Group Databasebeta

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C3×C5×Dic533 #44544279

order31980
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic533

Splittings

derived, HallC13×C41 ⋊ C3×C4×C5
HallC3×C5×C13×C41 ⋊ C4
HallC5×C13×C41 ⋊ C3×C4
HallC3×C13×C41 ⋊ C4×C5
HallC3×C5×C41 ⋊ Dic13
HallC5×C41 ⋊ C3×Dic13
HallC3×C5×C13 ⋊ Dic41
HallC3×C41 ⋊ C5×Dic13
HallC5×C13 ⋊ C3×Dic41
SylowC41 ⋊ C3×C5×Dic13
HallC3×C13 ⋊ C5×Dic41
SylowC13 ⋊ C3×C5×Dic41

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D533
commutator, hypocenterC13×C41C3×C4×C5
FrattiniC2C3×C5×D533
Fitting, socle, prime radicalC2×C3×C5×C13×C41C2
cosocleC2×C13×C41C2×C3×C5
LCSG ▷ C13×C41
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31980

Conjugacy classes & character table

8040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31980, 7);