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C5×D21×C19⋊C3 #26046196

order11970
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×D21×C19⋊C3
unambiguous semidirect productC3⋊(C5×D7×C19⋊C3)

Splittings

Fitting, socleC3×C5×C7×C19 ⋊ C2×C3
derivedC3×C7×C19 ⋊ C2×C3×C5
HallC3×C5×C7×C19⋊C3 ⋊ C2
HallC3×C7×C19⋊C3 ⋊ C2×C5
HallC3×C5×C19⋊C3 ⋊ D7
HallC5×C7×C19 ⋊ C3×D3
HallC3×C19⋊C3 ⋊ C5×D7
HallC7×C19 ⋊ C3×C5×D3
HallC5×C19 ⋊ C3×D21
HallC5×C7 ⋊ D3×C19⋊C3
SylowC19 ⋊ C3×C5×D21
SylowC7 ⋊ C5×D3×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC5D21×C19⋊C3
commutator, cosocle, hypocenterC3×C7×C19C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C19C2×C3
LCSG ▷ C3×C7×C19
UCSC1 ◁ C5

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

540 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×D21×D19⋊C3, C5×(C3⋊(D19⋊C3))⋊D7, C5×D3×D7×C19⋊C3, …
maximal normal subgroup ofC5×D21×D19⋊C3, C5×(C3⋊(D19⋊C3))⋊D7, C5×D3×D7×C19⋊C3, …
maximal quotient ofC5×C19⋊C3×Dic21, C2×C5×D21×C19⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 125);