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C43×D105 #22583288

order9030
isoclinismisoclinic class of D105
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C1

Aliases

direct productC43×D105
unambiguous semidirect productC3⋊(C43×D35)
unambiguous semidirect productC5⋊(D21×C43)
unambiguous semidirect productC7⋊(D15×C43)

Splittings

Fitting, socle, HallC3×C5×C7×C43 ⋊ C2
derived, HallC3×C5×C7 ⋊ C2×C43
HallC5×C7×C43 ⋊ D3
HallC3×C7×C43 ⋊ D5
HallC3×C5×C43 ⋊ D7
HallC7×C43 ⋊ D15
HallC5×C43 ⋊ D21
HallC3×C43 ⋊ D35
HallC5×C7 ⋊ D3×C43
HallC3×C7 ⋊ D5×C43
HallC3×C5 ⋊ D7×C43
SylowC7 ⋊ D15×C43
SylowC5 ⋊ D21×C43
SylowC3 ⋊ C43×D35

Subgroups

subgroupG/H
center, hypercenterC43D105
commutator, hypocenterC3×C5×C7C2×C43
FrattiniC1G
Fitting, socleC3×C5×C7×C43C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C43

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2322 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD43×D105, D7×D15×C43, D301⋊D15, …
maximal normal subgroup ofD43×D105, D7×D15×C43, D301⋊D15, …
maximal quotient ofC43×Dic105, C2×C43×D105, C43×D315, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9030, 21);