Finite Group Databasebeta

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C2×C3×C11×D39 #19104249

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

Aliases

direct productC2×C3×C11×D39
unambiguous semidirect product(C2×C3)⋊(C3×C11×D13)

Splittings

Fitting, socleC2×C32×C11×C13 ⋊ C2
derivedC3×C13 ⋊ C22×C3×C11
HallC32×C11×C13 ⋊ C22
HallC11×C13 ⋊ C2×C3×D3
HallC32×C13 ⋊ C22×C11
HallC32×C11 ⋊ C2×D13
SylowC13 ⋊ C2×C3×D3×C11
SylowC32 ⋊ C2×C11×D13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D39
commutator, hypocenterC3×C13C22×C3×C11
FrattiniC1G
Fitting, socleC2×C32×C11×C13C2
LCSG ▷ C3×C13
UCSC1 ◁ C2×C3×C11

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1386 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C11⋊C5×D39, C3×D5×C11×D39, C2×C3×C5×C11×D39, …
maximal normal subgroup ofC2×C3×C11⋊C5×D39, C2×C3×C5×C11×D39, C2×C3×C7×C11×D39
maximal quotient ofC3×D5×C11×D39, C2×C3×C5×C11×D39, C2×C3×C11×D195, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5148, 125);