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C5×D3×C7×D29 #27131773

order12180
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC5×D3×C7×D29

Splittings

Fitting, socle, HallC3×C5×C7×C29 ⋊ C22
derived, HallC3×C29 ⋊ C22×C5×C7
HallC5×C7×C29 ⋊ C2×D3
HallC3×C7×C29 ⋊ C22×C5
HallC3×C5×C29 ⋊ C22×C7
HallC7×C29 ⋊ C2×C5×D3
HallC5×C29 ⋊ C2×D3×C7
HallC3×C5×C7 ⋊ C2×D29
SylowC29 ⋊ C2×C5×D3×C7
HallC3×C7 ⋊ C2×C5×D29
HallC3×C5 ⋊ C2×C7×D29
SylowC3 ⋊ C2×C5×C7×D29

Subgroups

subgroupG/H
center, hypercenterC5×C7D3×D29
commutator, hypocenterC3×C29C22×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C29C22
LCSG ▷ C3×C29
UCSC1 ◁ C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1680 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×D9×D29, C5×D3×ΓL(1,𝔽8)×D29, C3×C5×D3×C7×D29, …
maximal normal subgroup ofC5×D3×ΓL(1,𝔽8)×D29, C3×C5×D3×C7×D29
maximal quotient ofC5×C7×D9×D29, C3×C5×D3×C7×D29, C5×D3×C7×D87, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 108);