Finite Group Databasebeta

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C2×C3×C5×D203 #27131827

order12180
isoclinismisoclinic class of D203
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×D203
unambiguous semidirect product(C2×C29)⋊(C3×C5×D7)

Splittings

Fitting, socleC2×C3×C5×C7×C29 ⋊ C2
derived, HallC7×C29 ⋊ C22×C3×C5
HallC3×C5×C7×C29 ⋊ C22
HallC5×C7×C29 ⋊ C22×C3
HallC3×C7×C29 ⋊ C22×C5
HallC3×C5×C29 ⋊ C2×D7
HallC5×C29 ⋊ C2×C3×D7
HallC3×C5×C7 ⋊ C2×D29
HallC3×C29 ⋊ C2×C5×D7
HallC5×C7 ⋊ C2×C3×D29
SylowC29 ⋊ C2×C3×C5×D7
HallC3×C7 ⋊ C2×C5×D29
SylowC7 ⋊ C2×C3×C5×D29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D203
commutator, hypocenterC7×C29C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C29C2
LCSG ▷ C7×C29
UCSC1 ◁ C2×C3×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3090 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C29⋊(D7⋊C9), C2×C5×C9×D203, C2×C3×C5×ΓL(1,𝔽8)⋊D29, …
maximal normal subgroup ofC2×C5×C29⋊(D7⋊C9), C2×C5×C9×D203, C2×C3×C5×ΓL(1,𝔽8)⋊D29, …
maximal quotient ofC2×C5×C9×D203, C3×C5×D3×D203, C2×C32×C5×D203, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 162);