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C7×D15×C13⋊C3 #22551269

order8190
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D15×C13⋊C3
unambiguous semidirect productC3⋊(C7×D5×C13⋊C3)
unambiguous semidirect productC5⋊(D3×C7×C13⋊C3)
unambiguous semidirect product(C13×D15)⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C13 ⋊ C2×C3
derivedC3×C5×C13 ⋊ C2×C3×C7
HallC3×C5×C7×C13⋊C3 ⋊ C2
HallC3×C7×C13⋊C3 ⋊ D5
HallC3×C5×C13⋊C3 ⋊ C2×C7
HallC5×C7×C13 ⋊ C3×D3
HallC3×C13⋊C3 ⋊ C7×D5
HallC7×C13 ⋊ C3×D15
HallC5×C13 ⋊ C3×D3×C7
HallC5×C7 ⋊ D3×C13⋊C3
SylowC13 ⋊ C3×C7×D15
SylowC5 ⋊ D3×C7×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC7D15×C13⋊C3
commutator, hypocenterC3×C5×C13C2×C3×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C13C2×C3
LCSG ▷ C3×C5×C13
UCSC1 ◁ C7

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

441 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×D15×D13⋊C3, D15×(C13⋊C3)⋊D7, D7×D15×C13⋊C3, …
maximal normal subgroup ofC7×D15×D13⋊C3, D15×(C13⋊C3)⋊D7, D7×D15×C13⋊C3, …
maximal quotient ofC7×C13⋊C3×Dic15, C2×C7×D15×C13⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8190, 103);