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C5×C3⋊Dic273 #30655278

order16380
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×C3⋊Dic273
unambiguous semidirect productC3⋊(C5×Dic273)
unambiguous semidirect productC7⋊(C5×C3⋊Dic39)

Splittings

derived, HallC32×C7×C13 ⋊ C4×C5
HallC32×C5×C7×C13 ⋊ C4
HallC32×C5×C13 ⋊ Dic7
HallC5×C7×C13 ⋊ C3⋊Dic3
HallC32×C5×C7 ⋊ Dic13
HallC32×C13 ⋊ C5×Dic7
HallC7×C13 ⋊ C5×C3⋊Dic3
HallC5×C13 ⋊ C3⋊Dic21
HallC32×C7 ⋊ C5×Dic13
HallC32×C5 ⋊ Dic91
HallC5×C7 ⋊ C3⋊Dic39
SylowC13 ⋊ C5×C3⋊Dic21
SylowC32 ⋊ C5×Dic91
SylowC7 ⋊ C5×C3⋊Dic39

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊D273
commutator, hypocenterC32×C7×C13C4×C5
FrattiniC2C5×C3⋊D273
Fitting, socle, prime radicalC2×C32×C5×C7×C13C2
cosocleC2×C32×C7×C13C2×C5
LCSG ▷ C32×C7×C13
UCSC1 ◁ C2×C5

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16380

Conjugacy classes & character table

4110 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 328);