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C5×Dic273 #19129674

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

Aliases

direct productC5×Dic273
unambiguous semidirect productC3⋊(C5×Dic91)
unambiguous semidirect productC7⋊(C5×Dic39)

Splittings

derived, HallC3×C7×C13 ⋊ C4×C5
HallC3×C5×C7×C13 ⋊ C4
HallC5×C7×C13 ⋊ Dic3
HallC3×C5×C13 ⋊ Dic7
HallC3×C5×C7 ⋊ Dic13
HallC7×C13 ⋊ C5×Dic3
HallC5×C13 ⋊ Dic21
HallC3×C13 ⋊ C5×Dic7
HallC5×C7 ⋊ Dic39
HallC3×C7 ⋊ C5×Dic13
HallC3×C5 ⋊ Dic91
SylowC13 ⋊ C5×Dic21
SylowC7 ⋊ C5×Dic39
SylowC3 ⋊ C5×Dic91

Subgroups

subgroupG/H
center, hypercenterC2×C5D273
commutator, hypocenterC3×C7×C13C4×C5
FrattiniC2C5×D273
Fitting, socleC2×C3×C5×C7×C13C2
LCSG ▷ C3×C7×C13
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1380 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×Dic819, C5×C3⋊#11763963, C5×C3⋊#11763964, …
maximal normal subgroup ofC5×C3⋊#11763963, C5×C3⋊#11763964, C5×C3⋊(ΓL(1,𝔽8)⋊Dic13), …
maximal quotient ofC5×Dic819, C3×C5×Dic273, C5×C3⋊Dic273, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 16);