Finite Group Databasebeta

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C3×C5×Dic3×C131 #37556078

order23580
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C131 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic3×C131
unambiguous semidirect productC3⋊(C3×C4×C5×C131)

Splittings

derivedC3 ⋊ C3×C4×C5×C131
HallC32×C5×C131 ⋊ C4
HallC32×C131 ⋊ C4×C5
HallC32×C5 ⋊ C4×C131
SylowC32 ⋊ C4×C5×C131

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C131D3
commutator, hypocenterC3C3×C4×C5×C131
FrattiniC2C3×C5×D3×C131
Fitting, socle, prime radicalC2×C32×C5×C131C2
cosocleC2×C3C2×C3×C5×C131
LCSG ▷ C3
UCSC1 ◁ C2×C3×C5×C131

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7860

Conjugacy classes & character table

11790 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23580, 53);