Finite Group Databasebeta

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C2×C3×C7×D145 #27131825

order12180
isoclinismisoclinic class of D145
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×D145
unambiguous semidirect product(C2×C5)⋊(C3×C7×D29)

Splittings

Fitting, socleC2×C3×C5×C7×C29 ⋊ C2
derived, HallC5×C29 ⋊ C22×C3×C7
HallC3×C5×C7×C29 ⋊ C22
HallC5×C7×C29 ⋊ C22×C3
HallC3×C7×C29 ⋊ C2×D5
HallC3×C5×C29 ⋊ C22×C7
HallC7×C29 ⋊ C2×C3×D5
HallC3×C5×C7 ⋊ C2×D29
HallC3×C29 ⋊ C2×C7×D5
HallC5×C7 ⋊ C2×C3×D29
SylowC29 ⋊ C2×C3×C7×D5
HallC3×C5 ⋊ C2×C7×D29
SylowC5 ⋊ C2×C3×C7×D29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D145
commutator, hypocenterC5×C29C22×C3×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C29C2
LCSG ▷ C5×C29
UCSC1 ◁ C2×C3×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3108 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7⋊C9×D145, C2×C7×C9×D145, C2×C3×ΓL(1,𝔽8)×D145, …
maximal normal subgroup ofC2×C7⋊C9×D145, C2×C7×C9×D145, C2×C3×ΓL(1,𝔽8)×D145, …
maximal quotient ofC2×C7×C9×D145, C3×D3×C7×D145, C2×C32×C7×D145, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 160);