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C3×D5×D203 #27131770

order12180
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC3×D5×D203
unambiguous semidirect product(D5×C29)⋊(C3×D7)

Splittings

Fitting, socle, HallC3×C5×C7×C29 ⋊ C22
derived, HallC5×C7×C29 ⋊ C22×C3
HallC3×C7×C29 ⋊ C2×D5
HallC3×C5×C29 ⋊ C2×D7
HallC7×C29 ⋊ C2×C3×D5
HallC5×C29 ⋊ C2×C3×D7
HallC3×C5×C7 ⋊ C2×D29
HallC3×C29 ⋊ D5×D7
HallC5×C7 ⋊ C2×C3×D29
SylowC29 ⋊ C3×D5×D7
HallC3×C7 ⋊ D5×D29
HallC3×C5 ⋊ C2×D203
SylowC7 ⋊ C3×D5×D29
SylowC5 ⋊ C2×C3×D203

Subgroups

subgroupG/H
center, hypercenterC3D5×D203
commutator, hypocenterC5×C7×C29C22×C3
FrattiniC1G
Fitting, socleC3×C5×C7×C29C22
LCSG ▷ C5×C7×C29
UCSC1 ◁ C3

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1236 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD5×C29⋊(D7⋊C9), C9×D5×D203, C3×D5×ΓL(1,𝔽8)⋊D29, …
maximal normal subgroup ofD5×C29⋊(D7⋊C9), C9×D5×D203, C3×D5×ΓL(1,𝔽8)⋊D29, …
maximal quotient ofC9×D5×D203, C32×D5×D203, C3×D15×D203, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 105);