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D5×#10587722 #19129763

order5460
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productD5×#10587722

Splittings

Fitting, socle, derived, HallC5×C7×C13 ⋊ C22×C3
HallD5×D91 ⋊ C3
HallC5×#63270 ⋊ C22
Hall#63270 ⋊ C2×D5
HallC7×C13 ⋊ C2×C3×D5
HallC5×C13 ⋊ C2×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×D13⋊C3
SylowC13 ⋊ D5×AGL(1,𝔽7)
SylowC7 ⋊ D5×D13⋊C3
SylowC5 ⋊ C2×#10587722

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C13C22×C3
LCSG ▷ C5×C7×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×ΓL(1,𝔽8)⋊(D13⋊C3), C3×D5×#10587722, D15×#10587722, …
maximal normal subgroup ofD5×ΓL(1,𝔽8)⋊(D13⋊C3), C3×D5×#10587722, C5×D5×#10587722, …
maximal quotient ofD5×#13109902, C3×D5×#10587722, D15×#10587722, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 105);