Finite Group Databasebeta

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C5×D21×C43 #22583284

order9030
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C2×C5×C43 · Schur multiplier (H2) = C1

Aliases

direct productC5×D21×C43
unambiguous semidirect productC3⋊(C5×D7×C43)
unambiguous semidirect productC7⋊(C5×D3×C43)

Splittings

Fitting, socle, HallC3×C5×C7×C43 ⋊ C2
derived, HallC3×C7 ⋊ C2×C5×C43
HallC5×C7×C43 ⋊ D3
HallC3×C7×C43 ⋊ C2×C5
HallC3×C5×C43 ⋊ D7
HallC7×C43 ⋊ C5×D3
HallC3×C43 ⋊ C5×D7
HallC3×C5×C7 ⋊ C2×C43
HallC5×C7 ⋊ D3×C43
HallC3×C5 ⋊ D7×C43
SylowC7 ⋊ C5×D3×C43
SylowC3 ⋊ C5×D7×C43

Subgroups

subgroupG/H
center, hypercenterC5×C43D21
commutator, hypocenterC3×C7C2×C5×C43
FrattiniC1G
Fitting, socleC3×C5×C7×C43C2
LCSG ▷ C3×C7
UCSC1 ◁ C5×C43

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2580 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D21×D43, C5×D3×D7×C43, C5×D21⋊D43, …
maximal normal subgroup ofC5×D21×D43, C5×D3×D7×C43, C5×D21⋊D43, …
maximal quotient ofC5×C43×Dic21, C2×C5×D21×C43, C5×C43×D63, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9030, 17);