Finite Group Databasebeta

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C13×C19×Dic15 #28414731

order14820
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C4×C13×C19 · Schur multiplier (H2) = C1

Aliases

direct productC13×C19×Dic15
unambiguous semidirect productC3⋊(C13×C19×Dic5)

Splittings

derived, HallC3×C5 ⋊ C4×C13×C19
HallC3×C5×C13×C19 ⋊ C4
HallC5×C13×C19 ⋊ Dic3
HallC3×C13×C19 ⋊ Dic5
HallC3×C5×C19 ⋊ C4×C13
HallC3×C5×C13 ⋊ C4×C19
HallC5×C19 ⋊ Dic3×C13
HallC5×C13 ⋊ Dic3×C19
HallC3×C19 ⋊ C13×Dic5
HallC3×C13 ⋊ C19×Dic5
SylowC5 ⋊ Dic3×C13×C19
SylowC3 ⋊ C13×C19×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C13×C19D15
commutator, hypocenterC3×C5C4×C13×C19
FrattiniC2C13×C19×D15
Fitting, socle, prime radicalC2×C3×C5×C13×C19C2
cosocleC2×C3×C5C2×C13×C19
LCSG ▷ C3×C5
UCSC1 ◁ C2×C13×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14820

Conjugacy classes & character table

4446 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 17);