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C7×C13×C3⋊D15 #22551307

order8190
isoclinismisoclinic class of C3⋊D15
automorphism?
homologyAbelianization (H1) = C2×C7×C13 · Schur multiplier (H2) = C3

Aliases

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

Splittings

Fitting, socle, HallC32×C5×C7×C13 ⋊ C2
derived, HallC32×C5 ⋊ C2×C7×C13
HallC32×C7×C13 ⋊ D5
HallC32×C5×C13 ⋊ C2×C7
HallC5×C7×C13 ⋊ C3⋊D3
HallC32×C5×C7 ⋊ C2×C13
HallC32×C13 ⋊ C7×D5
HallC5×C13 ⋊ C7×C3⋊D3
HallC32×C7 ⋊ D5×C13
HallC5×C7 ⋊ C13×C3⋊D3
SylowC32 ⋊ C7×D5×C13
SylowC5 ⋊ C7×C13×C3⋊D3

Subgroups

subgroupG/H
center, hypercenterC7×C13C3⋊D15
commutator, hypocenterC32×C5C2×C7×C13
FrattiniC1G
Fitting, socleC32×C5×C7×C13C2
LCSG ▷ C32×C5
UCSC1 ◁ C7×C13

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2184 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×D13×C3⋊D15, C13×D7×C3⋊D15, C3⋊D15×D91, …
maximal normal subgroup ofC7×D13×C3⋊D15, C13×D7×C3⋊D15, C3⋊D15×D91, …
maximal quotient ofC7×C13×C3⋊Dic15, C2×C7×C13×C3⋊D15

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8190, 141);