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C3×C13×Dic35 #19129669

order5460
isoclinismisoclinic class of D35
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C13×Dic35

Splittings

derived, HallC5×C7 ⋊ C3×C4×C13
HallC3×C5×C7×C13 ⋊ C4
HallC5×C7×C13 ⋊ C3×C4
HallC3×C7×C13 ⋊ Dic5
HallC3×C5×C13 ⋊ Dic7
HallC3×C5×C7 ⋊ C4×C13
HallC7×C13 ⋊ C3×Dic5
HallC5×C13 ⋊ C3×Dic7
HallC3×C7 ⋊ C13×Dic5
HallC3×C5 ⋊ C13×Dic7
SylowC7 ⋊ C3×C13×Dic5
SylowC5 ⋊ C3×C13×Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C13D35
commutator, hypocenterC5×C7C3×C4×C13
FrattiniC2C3×C13×D35
Fitting, socleC2×C3×C5×C7×C13C2
LCSG ▷ C5×C7
UCSC1 ◁ C2×C3×C13

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1482 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C13×Dic35, C13⋊C9×Dic35, C13×(C7⋊C9)⋊Dic5, …
maximal normal subgroup ofC9×C13×Dic35, C13⋊C9×Dic35, C13×(C7⋊C9)⋊Dic5, …
maximal quotient ofC9×C13×Dic35, C32×C13×Dic35, C3×C13×Dic105, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 11);