Finite Group Databasebeta

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C5×C7×D231 #30633579

order16170
isoclinismisoclinic class of D231
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×D231
unambiguous semidirect productC3⋊(C5×C7×D77)
unambiguous semidirect productC7⋊(C5×C7×D33)

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C2
derivedC3×C7×C11 ⋊ C2×C5×C7
HallC5×C72×C11 ⋊ D3
HallC3×C72×C11 ⋊ C2×C5
HallC3×C5×C72 ⋊ D11
HallC72×C11 ⋊ C5×D3
HallC5×C72 ⋊ D33
HallC3×C5×C11 ⋊ C7×D7
HallC3×C72 ⋊ C5×D11
HallC5×C11 ⋊ C7×D21
SylowC72 ⋊ C5×D33
HallC3×C11 ⋊ C5×C7×D7
HallC3×C5 ⋊ C7×D77
SylowC11 ⋊ C5×C7×D21
SylowC3 ⋊ C5×C7×D77

Subgroups

subgroupG/H
center, hypercenterC5×C7D231
commutator, cosocle, hypocenterC3×C7×C11C2×C5×C7
FrattiniC1G
Fitting, socleC3×C5×C72×C11C2
LCSG ▷ C3×C7×C11
UCSC1 ◁ C5×C7

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

4095 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×D11×D21, C5×C7×D7×D33, C5×D3×C7×D77, …
maximal normal subgroup ofC5×C7×D11×D21, C5×C7×D7×D33, C5×D3×C7×D77, …
maximal quotient ofC5×C7×Dic231, C2×C5×C7×D231

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 124);