Finite Group Databasebeta

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C5×#15688283 #28414741

order14820
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#15688283

Splittings

derived, HallC13×C19 ⋊ C3×C4×C5
HallC5×C19×Dic13 ⋊ C3
HallC5×#10625202 ⋊ C4
HallC5×C13×C19 ⋊ C3×C4
HallC19×Dic13 ⋊ C3×C5
Hall#10625202 ⋊ C4×C5
HallC5×Dic13 ⋊ C19⋊C3
HallC5×C19 ⋊ Dic13⋊C3
HallC5×C13 ⋊ C4×C19⋊C3
HallDic13 ⋊ C5×C19⋊C3
SylowC19 ⋊ C5×Dic13⋊C3
SylowC13 ⋊ C4×C5×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#13093364
commutator, hypocenterC13×C19C3×C4×C5
FrattiniC2C5×#13093364
Fitting, socleC2×C5×C13×C19C2×C3
prime radicalC2×C5×#10625202C2
cosocleC2×C13×C19C2×C3×C5
LCSG ▷ C13×C19
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4940

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14820, 27);