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C5×C3⋊D399 #26046221

order11970
automorphism?
homologyAbelianization (H1) = C2×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×C3⋊D399
unambiguous semidirect productC3⋊(C5×D399)
unambiguous semidirect productC7⋊(C5×C3⋊D57)
unambiguous semidirect productC19⋊(C5×C3⋊D21)

Splittings

Fitting, socle, HallC32×C5×C7×C19 ⋊ C2
derived, HallC32×C7×C19 ⋊ C2×C5
HallC32×C5×C19 ⋊ D7
HallC5×C7×C19 ⋊ C3⋊D3
HallC32×C5×C7 ⋊ D19
HallC32×C19 ⋊ C5×D7
HallC7×C19 ⋊ C5×C3⋊D3
HallC5×C19 ⋊ C3⋊D21
HallC32×C7 ⋊ C5×D19
HallC32×C5 ⋊ D133
HallC5×C7 ⋊ C3⋊D57
SylowC19 ⋊ C5×C3⋊D21
SylowC32 ⋊ C5×D133
SylowC7 ⋊ C5×C3⋊D57

Subgroups

subgroupG/H
center, hypercenterC5C3⋊D399
commutator, cosocle, hypocenterC32×C7×C19C2×C5
FrattiniC1G
Fitting, socleC32×C5×C7×C19C2
LCSG ▷ C32×C7×C19
UCSC1 ◁ C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3000 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×D399, C5×D21×D57, D15⋊D399, …
maximal normal subgroup ofC5×D3×D399, C5×D21×D57, D15⋊D399, …
maximal quotient ofC5×C3⋊Dic399, C2×C5×C3⋊D399

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 150);