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C3×C7×Dic65 #19129668

order5460
isoclinismisoclinic class of D65
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×Dic65

Splittings

derived, HallC5×C13 ⋊ C3×C4×C7
HallC3×C5×C7×C13 ⋊ C4
HallC5×C7×C13 ⋊ C3×C4
HallC3×C7×C13 ⋊ Dic5
HallC3×C5×C13 ⋊ C4×C7
HallC3×C5×C7 ⋊ Dic13
HallC7×C13 ⋊ C3×Dic5
HallC3×C13 ⋊ C7×Dic5
HallC5×C7 ⋊ C3×Dic13
HallC3×C5 ⋊ C7×Dic13
SylowC13 ⋊ C3×C7×Dic5
SylowC5 ⋊ C3×C7×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D65
commutator, hypocenterC5×C13C3×C4×C7
FrattiniC2C3×C7×D65
Fitting, socleC2×C3×C5×C7×C13C2
LCSG ▷ C5×C13
UCSC1 ◁ C2×C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1428 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×C9×Dic65, C7×Dic65⋊C9, C7⋊C9×Dic65, …
maximal normal subgroup ofC7×C9×Dic65, C7×Dic65⋊C9, C7⋊C9×Dic65, …
maximal quotient ofC7×C9×Dic65, C32×C7×Dic65, C3×C7×Dic195, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 10);