Finite Group Databasebeta

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C7×C22⋊(C13⋊(C52⋊C3)) #41032074

order27300
automorphism?
homologyAbelianization (H1) = C3×C7 · Schur multiplier (H2) = C2×C5

Aliases

direct productC7×C22⋊(C13⋊(C52⋊C3))
unambiguous semidirect productC22⋊(C7×C13⋊(C52⋊C3))
unambiguous semidirect productC13⋊(C7×C22⋊(C52⋊C3))
unambiguous semidirect productC52⋊(C7×C22⋊(C13⋊C3))

Splittings

Fitting, socle, HallC22×C52×C7×C13 ⋊ C3
derived, HallC22×C52×C13 ⋊ C3×C7
HallC52×C7×C13 ⋊ A4
HallC22×C52×C7 ⋊ C13⋊C3
HallC22×C7×C13 ⋊ C52⋊C3
HallC52×C13 ⋊ C7×A4
HallC52×C7 ⋊ C22⋊(C13⋊C3)
HallC22×C52 ⋊ C7×C13⋊C3
HallC7×C13 ⋊ C22⋊(C52⋊C3)
HallC22×C13 ⋊ C7×C52⋊C3
HallC22×C7 ⋊ C13⋊(C52⋊C3)
SylowC52 ⋊ C7×C22⋊(C13⋊C3)
SylowC13 ⋊ C7×C22⋊(C52⋊C3)
SylowC22 ⋊ C7×C13⋊(C52⋊C3)

Subgroups

subgroupG/H
center, hypercenterC7C22⋊(C13⋊(C52⋊C3))
commutator, cosocle, hypocenterC22×C52×C13C3×C7
FrattiniC1G
Fitting, socleC22×C52×C7×C13C3
LCSG ▷ C22×C52×C13
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

3052 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 964);