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C3×C5×D473 #28381990

order14190
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D473

Splittings

Fitting, socle, HallC3×C5×C11×C43 ⋊ C2
derived, HallC11×C43 ⋊ C2×C3×C5
HallC5×C11×C43 ⋊ C2×C3
HallC3×C11×C43 ⋊ C2×C5
HallC3×C5×C43 ⋊ D11
HallC5×C43 ⋊ C3×D11
HallC3×C5×C11 ⋊ D43
HallC3×C43 ⋊ C5×D11
HallC5×C11 ⋊ C3×D43
SylowC43 ⋊ C3×C5×D11
HallC3×C11 ⋊ C5×D43
SylowC11 ⋊ C3×C5×D43

Subgroups

subgroupG/H
center, hypercenterC3×C5D473
commutator, cosocle, hypocenterC11×C43C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C43C2
LCSG ▷ C11×C43
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7095

Conjugacy classes & character table

3570 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D11×D43, C3×D5×D473, C3×D55⋊D43, …
maximal normal subgroup ofC3×C5×D11×D43, C3×D5×D473, C3×D55⋊D43, …
maximal quotient ofC3×C5×Dic473, C2×C3×C5×D473

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14190, 7);