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C3×C5×Dic91 #19129666

order5460
isoclinismisoclinic class of D91
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic91

Splittings

derived, HallC7×C13 ⋊ C3×C4×C5
HallC3×C5×C7×C13 ⋊ C4
HallC5×C7×C13 ⋊ C3×C4
HallC3×C7×C13 ⋊ C4×C5
HallC3×C5×C13 ⋊ Dic7
HallC3×C5×C7 ⋊ Dic13
HallC5×C13 ⋊ C3×Dic7
HallC3×C13 ⋊ C5×Dic7
HallC5×C7 ⋊ C3×Dic13
HallC3×C7 ⋊ C5×Dic13
SylowC13 ⋊ C3×C5×Dic7
SylowC7 ⋊ C3×C5×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D91
commutator, hypocenterC7×C13C3×C4×C5
FrattiniC2C3×C5×D91
Fitting, socleC2×C3×C5×C7×C13C2
LCSG ▷ C7×C13
UCSC1 ◁ C2×C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1410 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C9×Dic91, C5×#15692563, C5×(C7⋊C9)⋊Dic13, …
maximal normal subgroup ofC5×C9×Dic91, C5×#15692563, C5×(C7⋊C9)⋊Dic13, …
maximal quotient ofC5×C9×Dic91, C32×C5×Dic91, C3×C5×Dic273, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 8);