Finite Group Databasebeta

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C13×(C3⋊D3)⋊D77 #49114965

order36036
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×(C3⋊D3)⋊D77
unambiguous semidirect product(C3⋊D3)⋊(C13×D77)

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C22
derived, HallC32×C7×C11 ⋊ C22×C13
HallC32×C11×C13 ⋊ C2×D7
HallC7×C11×C13 ⋊ D32
HallC32×C7×C13 ⋊ C2×D11
HallC11×C13 ⋊ (C3⋊D3)⋊D7
HallC32×C13 ⋊ C2×D77
HallC32×C11 ⋊ C2×C13×D7
HallC7×C13 ⋊ (C3⋊D3)⋊D11
HallC7×C11 ⋊ D32×C13
HallC32×C7 ⋊ C2×C13×D11
SylowC11 ⋊ C13×(C3⋊D3)⋊D7
SylowC32 ⋊ C2×C13×D77
SylowC7 ⋊ C13×(C3⋊D3)⋊D11

Subgroups

subgroupG/H
center, hypercenterC13(C3⋊D3)⋊D77
commutator, cosocle, hypocenterC32×C7×C11C22×C13
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C32×C7×C11
UCSC1 ◁ C13

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

3081 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 633);