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D15×#63270 #22551279

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

Aliases

direct productD15×#63270
unambiguous semidirect productC3⋊(D5×#63270)
unambiguous semidirect productC5⋊(D3×#63270)

Splittings

Fitting, socle, derivedC3×C5×C7×C13 ⋊ C2×C3
HallC3×C5×#63270 ⋊ C2
HallC3×#63270 ⋊ 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×#63270

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×#10587722, D15×#10587720, D15×#10587716, …
maximal normal subgroup ofD15×#10587722, D15×#10587720, D15×#10587716, …
maximal quotient ofDic15×#63270, C2×D15×#63270

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8190, 113);