Finite Group Databasebeta

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C5×D32×C11×C13 #38788222

order25740
automorphism?
homologyAbelianization (H1) = C22×C5×C11×C13 · Schur multiplier (H2) = C2

Aliases

direct productC5×D32×C11×C13
unambiguous semidirect product(C3×D3)⋊(C2×C5×C11×C13)
unambiguous semidirect product(C3⋊D3)⋊(C2×C5×C11×C13)

Splittings

Fitting, socle, HallC32×C5×C11×C13 ⋊ C22
derived, SylowC32 ⋊ C22×C5×C11×C13
HallC32×C11×C13 ⋊ C22×C5
HallC32×C5×C13 ⋊ C22×C11
HallC32×C5×C11 ⋊ C22×C13
HallC32×C13 ⋊ C22×C5×C11
HallC32×C11 ⋊ C22×C5×C13
HallC32×C5 ⋊ C22×C11×C13

Subgroups

subgroupG/H
center, hypercenterC5×C11×C13D32
commutator, cosocle, hypocenterC32C22×C5×C11×C13
FrattiniC1G
Fitting, socleC32×C5×C11×C13C22
LCSG ▷ C32
UCSC1 ◁ C5×C11×C13

176 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 4290

Conjugacy classes & character table

6435 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 453);