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C7×D15⋊D29 #27131799

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

Aliases

direct productC7×D15⋊D29
unambiguous semidirect productD15⋊(C7×D29)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC7D15⋊D29
commutator, hypocenterC3×C5×C29C22×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C29C22
LCSG ▷ C3×C5×C29
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

966 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×D45⋊D29, ΓL(1,𝔽8)×D15⋊D29, C3×C7×D15⋊D29, …
maximal normal subgroup ofΓL(1,𝔽8)×D15⋊D29, C3×C7×D15⋊D29
maximal quotient ofC7×D45⋊D29, C3×C7×D15⋊D29, C7×D87⋊D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 134);