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C7×Dic5×C13⋊C3 #19129691

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

Aliases

direct productC7×Dic5×C13⋊C3
unambiguous semidirect product(C13×Dic5)⋊(C3×C7)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C7D5×C13⋊C3
commutator, hypocenterC5×C13C3×C4×C7
FrattiniC2C7×D5×C13⋊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

392 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofDic5×ΓL(1,𝔽8)×C13⋊C3, C3×C7×Dic5×C13⋊C3, C7×C13⋊C3×Dic15, …
maximal normal subgroup ofDic5×ΓL(1,𝔽8)×C13⋊C3, C3×C7×Dic5×C13⋊C3, C5×C7×Dic5×C13⋊C3, …
maximal quotient ofC7×Dic5×C13⋊C9, C3×C7×Dic5×C13⋊C3, C7×C13⋊C3×Dic15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 33);