Finite Group Databasebeta

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C7×C11×D105 #30633574

order16170
isoclinismisoclinic class of D105
automorphism?
homologyAbelianization (H1) = C2×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×D105
unambiguous semidirect productC3⋊(C7×C11×D35)
unambiguous semidirect productC5⋊(C7×C11×D21)
unambiguous semidirect productC7⋊(C7×C11×D15)

Splittings

Fitting, socle, HallC3×C5×C72×C11 ⋊ C2
derivedC3×C5×C7 ⋊ C2×C7×C11
HallC5×C72×C11 ⋊ D3
HallC3×C72×C11 ⋊ D5
HallC3×C5×C72 ⋊ C2×C11
HallC72×C11 ⋊ D15
HallC5×C72 ⋊ D3×C11
HallC3×C5×C11 ⋊ C7×D7
HallC3×C72 ⋊ D5×C11
HallC5×C11 ⋊ C7×D21
SylowC72 ⋊ C11×D15
HallC3×C11 ⋊ C7×D35
HallC3×C5 ⋊ C7×C11×D7
SylowC5 ⋊ C7×C11×D21
SylowC3 ⋊ C7×C11×D35

Subgroups

subgroupG/H
center, hypercenterC7×C11D105
commutator, cosocle, hypocenterC3×C5×C7C2×C7×C11
FrattiniC1G
Fitting, socleC3×C5×C72×C11C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C7×C11

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

4158 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D11×D105, C7×C11×D7×D15, C7×D77⋊D15, …
maximal normal subgroup ofC7×D11×D105, C7×C11×D7×D15, C7×D77⋊D15, …
maximal quotient ofC7×C11×Dic105, C2×C7×C11×D105

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 119);