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D15×D203 #27131794

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

Aliases

direct productD15×D203

Splittings

Fitting, socle, derived, HallC3×C5×C7×C29 ⋊ C22
HallC5×C7×C29 ⋊ C2×D3
HallC3×C7×C29 ⋊ C2×D5
HallC3×C5×C29 ⋊ C2×D7
HallC7×C29 ⋊ C2×D15
HallC5×C29 ⋊ D3×D7
HallC3×C5×C7 ⋊ C2×D29
HallC3×C29 ⋊ D5×D7
HallC5×C7 ⋊ D3×D29
SylowC29 ⋊ D7×D15
HallC3×C7 ⋊ D5×D29
HallC3×C5 ⋊ C2×D203
SylowC7 ⋊ D15×D29
SylowC5 ⋊ D3×D203
SylowC3 ⋊ D5×D203

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C7×C29C22
LCSG ▷ C3×C5×C7×C29
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

927 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD45×D203, D15×ΓL(1,𝔽8)⋊D29, C3×D15×D203, …
maximal normal subgroup ofD15×ΓL(1,𝔽8)⋊D29, C3×D15×D203
maximal quotient ofD45×D203, C3×D15×D203, #49141614, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 129);