Finite Group Databasebeta

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C5×C7×Dic39 #19129672

order5460
isoclinismisoclinic class of D39
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×Dic39
unambiguous semidirect productC3⋊(C5×C7×Dic13)

Splittings

derived, HallC3×C13 ⋊ C4×C5×C7
HallC3×C5×C7×C13 ⋊ C4
HallC5×C7×C13 ⋊ Dic3
HallC3×C7×C13 ⋊ C4×C5
HallC3×C5×C13 ⋊ C4×C7
HallC3×C5×C7 ⋊ Dic13
HallC7×C13 ⋊ C5×Dic3
HallC5×C13 ⋊ C7×Dic3
HallC3×C7 ⋊ C5×Dic13
HallC3×C5 ⋊ C7×Dic13
SylowC13 ⋊ C5×C7×Dic3
SylowC3 ⋊ C5×C7×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D39
commutator, hypocenterC3×C13C4×C5×C7
FrattiniC2C5×C7×D39
Fitting, socleC2×C3×C5×C7×C13C2
LCSG ▷ C3×C13
UCSC1 ◁ C2×C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1470 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×Dic117, C5×C7×C3⋊(Dic13⋊C3), C5×C3⋊#11763957, …
maximal normal subgroup ofC5×C7×C3⋊(Dic13⋊C3), C5×C3⋊#11763957, C5×C3⋊#11763958, …
maximal quotient ofC5×C7×Dic117, C3×C5×C7×Dic39, C5×C7×C3⋊Dic39, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 14);