Finite Group Databasebeta

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C11×D21⋊D39 #49114959

order36036
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D21⋊D39
unambiguous semidirect productD21⋊(C11×D39)

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C22
derived, HallC32×C7×C13 ⋊ C22×C11
HallC32×C11×C13 ⋊ C2×D7
HallC7×C11×C13 ⋊ D32
HallC32×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ (C3⋊D3)⋊D7
HallC32×C13 ⋊ C2×C11×D7
HallC32×C11 ⋊ D7×D13
HallC7×C13 ⋊ D32×C11
HallC7×C11 ⋊ D3×D39
HallC32×C7 ⋊ C2×C11×D13
SylowC13 ⋊ C11×(C3⋊D3)⋊D7
SylowC32 ⋊ C11×D7×D13
SylowC7 ⋊ D3×C11×D39

Subgroups

subgroupG/H
center, hypercenterC11D21⋊D39
commutator, cosocle, hypocenterC32×C7×C13C22×C11
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C32×C7×C13
UCSC1 ◁ C11

176 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6006

Conjugacy classes & character table

2673 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 627);