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C7×C3⋊#63122 #19129840

order5460
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊#63122
unambiguous semidirect productC3⋊(C7×#63122)

Splittings

Fitting, socle, HallC3×C5×C7×C13 ⋊ C4
derived, HallC3×C5×C13 ⋊ C4×C7
HallC5×C7×C13 ⋊ Dic3
HallC3×C7×C13 ⋊ AGL(1,𝔽5)
HallC3×C5×C7 ⋊ #261
HallC7×C13 ⋊ ΓL(1,𝔽16)
HallC5×C13 ⋊ C7×Dic3
HallC3×C13 ⋊ C7×AGL(1,𝔽5)
HallC5×C7 ⋊ C3⋊#261
HallC3×C7 ⋊ #63122
HallC3×C5 ⋊ C7×#261
SylowC13 ⋊ C7×ΓL(1,𝔽16)
SylowC5 ⋊ C7×C3⋊#261
SylowC3 ⋊ C7×#63122

Subgroups

subgroupG/H
center, hypercenterC7C3⋊#63122
commutator, hypocenterC3×C5×C13C4×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C13C4
LCSG ▷ C3×C5×C13
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

378 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×C9⋊#63122, C7×C3⋊(#63122⋊C3), C3⋊#19129737, …
maximal normal subgroup ofC7×C3⋊(#63122⋊C3), C3⋊#19129737, C3⋊#19129739, …
maximal quotient ofC7×C9⋊#63122, C3×C7×C3⋊#63122, C7×C3⋊(C3⋊#63122), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 182);