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C5×C11×C37⋊C3 #20259138

order6105
isoclinismisoclinic class of C37⋊C3
automorphism?
homologyAbelianization (H1) = C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×C37⋊C3
unambiguous semidirect productC37⋊(C3×C5×C11)
unambiguous semidirect product(C5×C37)⋊(C3×C11)
unambiguous semidirect product(C5×C11×C37)⋊C3

Splittings

Fitting, socle, HallC5×C11×C37 ⋊ C3
derived, SylowC37 ⋊ C3×C5×C11
HallC11×C37 ⋊ C3×C5
HallC5×C37 ⋊ C3×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11C37⋊C3
commutator, hypocenterC37C3×C5×C11
FrattiniC1G
Fitting, socleC5×C11×C37C3
LCSG ▷ C37
UCSC1 ◁ C5×C11

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

825 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C5×C11×C37⋊C3, C5×C11×D37⋊C3, C5×D11×C37⋊C3, …
maximal normal subgroup ofC2×C5×C11×C37⋊C3, C5×C11×D37⋊C3, C5×D11×C37⋊C3, …
maximal quotient ofC2×C5×C11×C37⋊C3, C5×C11×#66524, C3×C5×C11×C37⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6105, 3);