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C13×(C19⋊C3)⋊Dic5 #28414751

order14820
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×(C19⋊C3)⋊Dic5
unambiguous semidirect product(C19⋊C3)⋊(C13×Dic5)
unambiguous semidirect productDic95⋊(C3×C13)

Splittings

derived, HallC5×C19 ⋊ C3×C4×C13
HallC13×Dic95 ⋊ C3
HallC5×C13×C19⋊C3 ⋊ C4
HallC5×C13×C19 ⋊ C3×C4
HallC13×C19⋊C3 ⋊ Dic5
HallDic95 ⋊ C3×C13
HallC5×C19⋊C3 ⋊ C4×C13
HallC13×C19 ⋊ C3×Dic5
HallC5×C13 ⋊ (C19⋊C3)⋊C4
HallC19⋊C3 ⋊ C13×Dic5
SylowC19 ⋊ C3×C13×Dic5
SylowC5 ⋊ C13×(C19⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C13C5⋊(D19⋊C3)
commutator, hypocenterC5×C19C3×C4×C13
FrattiniC2C13×C5⋊(D19⋊C3)
Fitting, socleC2×C5×C13×C19C2×C3
prime radicalC2×C5×C13×C19⋊C3C2
cosocleC2×C5×C19C2×C3×C13
LCSG ▷ C5×C19
UCSC1 ◁ C2×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4940

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 37);