Finite Group Databasebeta

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C32×D77⋊D13 #49114899

order36036
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3

Aliases

direct productC32×D77⋊D13

Splittings

Fitting, socle, HallC32×C7×C11×C13 ⋊ C22
derived, HallC7×C11×C13 ⋊ C22×C32
HallC32×C11×C13 ⋊ C2×D7
HallC32×C7×C13 ⋊ C2×D11
HallC32×C7×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C32×D7
HallC32×C13 ⋊ D7×D11
HallC32×C11 ⋊ D7×D13
HallC7×C13 ⋊ C2×C32×D11
HallC7×C11 ⋊ C2×C32×D13
HallC32×C7 ⋊ D11×D13
SylowC13 ⋊ C32×D7×D11
SylowC11 ⋊ C32×D7×D13
SylowC7 ⋊ C32×D11×D13

Subgroups

subgroupG/H
center, hypercenterC32D77⋊D13
commutator, cosocle, hypocenterC7×C11×C13C22×C32
FrattiniC1G
Fitting, socleC32×C7×C11×C13C22
LCSG ▷ C7×C11×C13
UCSC1 ◁ C32

240 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 9009

Conjugacy classes & character table

2475 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 567);