Finite Group Databasebeta

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C3×C7×D205 #22575552

order8610
isoclinismisoclinic class of D205
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D205
unambiguous semidirect productC5⋊(C3×C7×D41)
unambiguous semidirect productC41⋊(C3×C7×D5)

Splittings

Fitting, socle, HallC3×C5×C7×C41 ⋊ C2
derived, HallC5×C41 ⋊ C2×C3×C7
HallC5×C7×C41 ⋊ C2×C3
HallC3×C7×C41 ⋊ D5
HallC3×C5×C41 ⋊ C2×C7
HallC7×C41 ⋊ C3×D5
HallC3×C41 ⋊ C7×D5
HallC3×C5×C7 ⋊ D41
SylowC41 ⋊ C3×C7×D5
HallC5×C7 ⋊ C3×D41
HallC3×C5 ⋊ C7×D41
SylowC5 ⋊ C3×C7×D41

Subgroups

subgroupG/H
center, hypercenterC3×C7D205
commutator, hypocenterC5×C41C2×C3×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C41C2
LCSG ▷ C5×C41
UCSC1 ◁ C3×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C7×#11717961, C3×C7×#11717962, C3×C7⋊#11717961, …
maximal normal subgroup ofC3×C7×#11717961, C3×C7×#11717962, C3×C7⋊#11717961, …
maximal quotient ofC3×C7×Dic205, C2×C3×C7×D205, C7×C9×D205, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8610, 9);