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C5×#11763962 #19129686

order5460
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#11763962

Splittings

derived, HallC7×C13 ⋊ C3×C4×C5
HallC5×C13×Dic7 ⋊ C3
HallC5×#63271 ⋊ C4
HallC5×C7×C13 ⋊ C3×C4
HallC13×Dic7 ⋊ C3×C5
Hall#63271 ⋊ C4×C5
HallC5×Dic7 ⋊ C13⋊C3
HallC5×C13 ⋊ ΓL(1,𝔽8)⋊C4
HallC5×C7 ⋊ C4×C13⋊C3
HallDic7 ⋊ C5×C13⋊C3
SylowC13 ⋊ C5×ΓL(1,𝔽8)⋊C4
SylowC7 ⋊ C4×C5×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#10587721
commutator, hypocenterC7×C13C3×C4×C5
FrattiniC2C5×#10587721
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

270 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C13⋊C3×ΓL(1,𝔽8)⋊C4, C3×C5×#11763962, C5×C3⋊#11763962, …
maximal normal subgroup ofC5×C13⋊C3×ΓL(1,𝔽8)⋊C4, C3×C5×#11763962, C25×#11763962, …
maximal quotient ofC5×#15692570, C3×C5×#11763962, C5×C3⋊#11763962, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 28);