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D15×D209 #27160073

order12540
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD15×D209

Splittings

Fitting, socle, derived, HallC3×C5×C11×C19 ⋊ C22
HallC5×C11×C19 ⋊ C2×D3
HallC3×C11×C19 ⋊ C2×D5
HallC3×C5×C19 ⋊ C2×D11
HallC11×C19 ⋊ C2×D15
HallC3×C5×C11 ⋊ C2×D19
HallC5×C19 ⋊ D3×D11
HallC3×C19 ⋊ D5×D11
HallC5×C11 ⋊ D3×D19
HallC3×C11 ⋊ D5×D19
SylowC19 ⋊ D11×D15
HallC3×C5 ⋊ C2×D209
SylowC11 ⋊ D15×D19
SylowC5 ⋊ D3×D209
SylowC3 ⋊ D5×D209

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C11×C19C22
LCSG ▷ C3×C5×C11×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

954 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD45×D209, D15×C11⋊(D19⋊C3), C3×D15×D209, …
maximal normal subgroup ofD15×C11⋊(D19⋊C3), C3×D15×D209
maximal quotient ofD45×D209, C3×D15×D209, #49178720, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12540, 103);