Finite Group Databasebeta

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C5×C7×D129 #22583283

order9030
isoclinismisoclinic class of D129
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×D129
unambiguous semidirect productC3⋊(C5×C7×D43)

Splittings

Fitting, socle, HallC3×C5×C7×C43 ⋊ C2
derived, HallC3×C43 ⋊ C2×C5×C7
HallC5×C7×C43 ⋊ D3
HallC3×C7×C43 ⋊ C2×C5
HallC3×C5×C43 ⋊ C2×C7
HallC7×C43 ⋊ C5×D3
HallC5×C43 ⋊ D3×C7
HallC3×C5×C7 ⋊ D43
SylowC43 ⋊ C5×D3×C7
HallC3×C7 ⋊ C5×D43
HallC3×C5 ⋊ C7×D43
SylowC3 ⋊ C5×C7×D43

Subgroups

subgroupG/H
center, hypercenterC5×C7D129
commutator, hypocenterC3×C43C2×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C43C2
LCSG ▷ C3×C43
UCSC1 ◁ C5×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2310 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×C7×D43, C5×D7×D129, C5×D21⋊D43, …
maximal normal subgroup ofC5×D3×C7×D43, C5×D7×D129, C5×D21⋊D43, …
maximal quotient ofC5×C7×Dic129, C2×C5×C7×D129, C5×C7×D387, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9030, 16);