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C3×C5⋊#11716321 #26046174

order11970
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5⋊#11716321
unambiguous semidirect productC5⋊(C3×#11716321)

Splittings

Fitting, socleC3×C5×C7×C19 ⋊ C2×C3
derived, HallC5×C7×C19 ⋊ C2×C32
HallC3×C5×#87704 ⋊ C2
HallC7×D95 ⋊ C32
HallC3×#87704 ⋊ D5
HallD95 ⋊ C3×ΓL(1,𝔽8)
HallC7×C19 ⋊ C32×D5
HallC5×C19 ⋊ C2×C3×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×D19⋊C3
SylowC19 ⋊ C3×D5×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C5⋊(D19⋊C3)
SylowC5 ⋊ C3×#11716321

Subgroups

subgroupG/H
center, hypercenterC3C5⋊#11716321
commutator, cosocle, hypocenterC5×C7×C19C2×C32
FrattiniC1G
Fitting, socleC3×C5×C7×C19C2×C3
LCSG ▷ C5×C7×C19
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

375 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#11716325⋊D5, C3×#11716327⋊D5, C3×D5×#11716321, …
maximal normal subgroup ofC3×#11716325⋊D5, C3×#11716327⋊D5, C3×D5×#11716321, …
maximal quotient ofC3×#22547614, C2×C3×C5⋊#11716321

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11970, 103);