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C2×C3×C5×C7×D29 #27131829

order12180
isoclinismisoclinic class of D29
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×C7×D29

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C7D29
commutator, hypocenterC29C22×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C29C2
LCSG ▷ C29
UCSC1 ◁ C2×C3×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×D29×C7⋊C9, C2×C5×C7×C9×D29, C2×C3×C5×ΓL(1,𝔽8)×D29, …
maximal normal subgroup ofC2×C5×D29×C7⋊C9, C2×C5×C7×C9×D29, C2×C3×C5×ΓL(1,𝔽8)×D29, …
maximal quotient ofC2×C5×C7×C9×D29, C3×C5×D3×C7×D29, C2×C32×C5×C7×D29, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 164);