Finite Group Databasebeta

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D5×D399 #22547729

order7980
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD5×D399
unambiguous semidirect product(C3×D5)⋊D133
unambiguous semidirect product(C7×D5)⋊D57
unambiguous semidirect product(D5×C19)⋊D21

Splittings

Fitting, socle, derived, HallC3×C5×C7×C19 ⋊ C22
HallC5×C7×C19 ⋊ C2×D3
HallC3×C7×C19 ⋊ C2×D5
HallC3×C5×C19 ⋊ C2×D7
HallC7×C19 ⋊ D3×D5
HallC3×C5×C7 ⋊ C2×D19
HallC5×C19 ⋊ C2×D21
HallC3×C19 ⋊ D5×D7
HallC5×C7 ⋊ C2×D57
HallC3×C7 ⋊ D5×D19
SylowC19 ⋊ D5×D21
HallC3×C5 ⋊ C2×D133
SylowC7 ⋊ D5×D57
SylowC5 ⋊ C2×D399
SylowC3 ⋊ D5×D133

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C7×C19C22
LCSG ▷ C3×C5×C7×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

804 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×D1197, D5×C3⋊#11716327, D5×C3⋊#11716328, …
maximal normal subgroup ofD5×C3⋊#11716327, D5×C3⋊#11716328, D5×C3⋊(ΓL(1,𝔽8)⋊D19), …
maximal quotient ofD5×D1197, C3×D5×D399, D15×D399, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 154);