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C7×#63118⋊C3 #19129752

order5460
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×#63118⋊C3
unambiguous semidirect product#63118⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C7×C13 ⋊ C3×C4
derived, HallC5×C13 ⋊ C3×C4×C7
HallC7×#63118 ⋊ C3
HallC5×C7×C13⋊C3 ⋊ C4
HallC7×C13⋊C3 ⋊ Dic5
Hall#63118 ⋊ C3×C7
HallC5×C13⋊C3 ⋊ C4×C7
HallC7×C13 ⋊ C3×Dic5
HallC13⋊C3 ⋊ C7×Dic5
HallC5×C7 ⋊ AGL(1,𝔽13)
SylowC13 ⋊ C3×C7×Dic5
SylowC5 ⋊ C7×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC7#63118⋊C3
commutator, hypocenterC5×C13C3×C4×C7
FrattiniC1G
Fitting, socleC5×C7×C13C3×C4
LCSG ▷ C5×C13
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

203 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)×#63118⋊C3, C3×C7×#63118⋊C3, C7×C3⋊(#63118⋊C3), …
maximal normal subgroup ofΓL(1,𝔽8)×#63118⋊C3, C3×C7×#63118⋊C3, C5×C7×#63118⋊C3, …
maximal quotient ofC7×#63118⋊C9, C3×C7×#63118⋊C3, C7×C3⋊(#63118⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 94);