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C5×D21×C71 #28415853

order14910
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C2×C5×C71 · Schur multiplier (H2) = C1

Aliases

direct productC5×D21×C71
unambiguous semidirect productC3⋊(C5×D7×C71)
unambiguous semidirect productC7⋊(C5×D3×C71)

Splittings

Fitting, socle, HallC3×C5×C7×C71 ⋊ C2
derived, HallC3×C7 ⋊ C2×C5×C71
HallC5×C7×C71 ⋊ D3
HallC3×C7×C71 ⋊ C2×C5
HallC3×C5×C71 ⋊ D7
HallC7×C71 ⋊ C5×D3
HallC3×C71 ⋊ C5×D7
HallC3×C5×C7 ⋊ C2×C71
HallC5×C7 ⋊ D3×C71
HallC3×C5 ⋊ D7×C71
SylowC7 ⋊ C5×D3×C71
SylowC3 ⋊ C5×D7×C71

Subgroups

subgroupG/H
center, hypercenterC5×C71D21
commutator, cosocle, hypocenterC3×C7C2×C5×C71
FrattiniC1G
Fitting, socleC3×C5×C7×C71C2
LCSG ▷ C3×C7
UCSC1 ◁ C5×C71

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7455

Conjugacy classes & character table

4260 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D21×D71, C5×D3×D7×C71, C5×D21⋊D71, …
maximal normal subgroup ofC5×D21×D71, C5×D3×D7×C71, C5×D21⋊D71, …
maximal quotient ofC5×C71×Dic21, C2×C5×D21×C71

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14910, 16);