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D15×#63271 #22551280

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

Aliases

direct productD15×#63271
unambiguous semidirect productC3⋊(D5×#63271)
unambiguous semidirect productC5⋊(D3×#63271)

Splittings

Fitting, socle, derivedC3×C5×C7×C13 ⋊ C2×C3
HallC3×C5×#63271 ⋊ C2
HallC3×#63271 ⋊ D5
HallC5×C7×C13 ⋊ C3×D3
HallC7×C13 ⋊ C3×D15
HallC5×C13 ⋊ D3×ΓL(1,𝔽8)
HallC5×C7 ⋊ D3×C13⋊C3
SylowC13 ⋊ ΓL(1,𝔽8)×D15
SylowC7 ⋊ D15×C13⋊C3
SylowC5 ⋊ D3×#63271

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C7×C13C2×C3
LCSG ▷ C3×C5×C7×C13
UCSC1

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

297 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD15×#10587723, D15×#10587721, D15×#10587717, …
maximal normal subgroup ofD15×#10587723, D15×#10587721, D15×#10587717, …
maximal quotient ofDic15×#63271, C2×D15×#63271

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8190, 114);