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C2×C11×C3⋊D39 #19104245

order5148
isoclinismisoclinic class of C3⋊D39
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C11×C3⋊D39
unambiguous semidirect product(C2×C3)⋊(C11×D39)
unambiguous semidirect product(C2×C13)⋊(C11×C3⋊D3)

Splittings

Fitting, socleC2×C32×C11×C13 ⋊ C2
derived, HallC32×C13 ⋊ C22×C11
HallC32×C11×C13 ⋊ C22
HallC11×C13 ⋊ C2×C3⋊D3
HallC32×C11 ⋊ C2×D13
SylowC13 ⋊ C2×C11×C3⋊D3
SylowC32 ⋊ C2×C11×D13

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊D39
commutator, hypocenterC32×C13C22×C11
FrattiniC1G
Fitting, socleC2×C32×C11×C13C2
LCSG ▷ C32×C13
UCSC1 ◁ C2×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11⋊C5×C3⋊D39, D5×C11×C3⋊D39, C2×C5×C11×C3⋊D39, …
maximal normal subgroup ofC2×C11⋊C5×C3⋊D39, C2×C5×C11×C3⋊D39, C2×C7×C11×C3⋊D39
maximal quotient ofD5×C11×C3⋊D39, C2×C5×C11×C3⋊D39, C2×C11×C3⋊D195, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 121);