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C5×C11×D69 #21439102

order7590
isoclinismisoclinic class of D69
automorphism?
homologyAbelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D69
unambiguous semidirect productC3⋊(C5×C11×D23)

Splittings

Fitting, socle, HallC3×C5×C11×C23 ⋊ C2
derived, HallC3×C23 ⋊ C2×C5×C11
HallC5×C11×C23 ⋊ D3
HallC3×C11×C23 ⋊ C2×C5
HallC3×C5×C23 ⋊ C2×C11
HallC11×C23 ⋊ C5×D3
HallC3×C5×C11 ⋊ D23
HallC5×C23 ⋊ D3×C11
HallC3×C11 ⋊ C5×D23
SylowC23 ⋊ C5×D3×C11
HallC3×C5 ⋊ C11×D23
SylowC3 ⋊ C5×C11×D23

Subgroups

subgroupG/H
center, hypercenterC5×C11D69
commutator, hypocenterC3×C23C2×C5×C11
FrattiniC1G
Fitting, socleC3×C5×C11×C23C2
LCSG ▷ C3×C23
UCSC1 ◁ C5×C11

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1980 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×C11×D23, C5×D11×D69, C5×D33⋊D23, …
maximal normal subgroup ofC5×D3×C11×D23, C5×D11×D69, C5×D33⋊D23, …
maximal quotient ofC5×C11×Dic69, C2×C5×C11×D69, C5×C11×D207, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7590, 12);