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C7×Dic65⋊C3 #19129695

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

Aliases

direct productC7×Dic65⋊C3
unambiguous semidirect productDic65⋊(C3×C7)

Splittings

derived, HallC5×C13 ⋊ C3×C4×C7
HallC7×Dic65 ⋊ C3
HallC5×C7×C13⋊C3 ⋊ C4
HallC5×C7×C13 ⋊ C3×C4
HallC7×C13⋊C3 ⋊ Dic5
HallDic65 ⋊ C3×C7
HallC5×C13⋊C3 ⋊ C4×C7
HallC7×C13 ⋊ C3×Dic5
HallC13⋊C3 ⋊ C7×Dic5
HallC5×C7 ⋊ Dic13⋊C3
SylowC13 ⋊ C3×C7×Dic5
SylowC5 ⋊ C7×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C7C5⋊(D13⋊C3)
commutator, hypocenterC5×C13C3×C4×C7
FrattiniC2C7×C5⋊(D13⋊C3)
Fitting, socleC2×C5×C7×C13C2×C3
LCSG ▷ C5×C13
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)×Dic65⋊C3, C3×C7×Dic65⋊C3, C7×C3⋊(Dic65⋊C3), …
maximal normal subgroup ofΓL(1,𝔽8)×Dic65⋊C3, C3×C7×Dic65⋊C3, C5×C7×Dic65⋊C3, …
maximal quotient ofC7×Dic65⋊C9, C3×C7×Dic65⋊C3, C7×C3⋊(Dic65⋊C3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 37);