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C52×C22⋊(C109⋊C3) #45658366

order32700
automorphism?
homologyAbelianization (H1) = C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC52×C22⋊(C109⋊C3)
unambiguous semidirect productC22⋊(C52×C109⋊C3)
unambiguous semidirect product(C22×C5)⋊(C5×C109⋊C3)
unambiguous semidirect productC109⋊(C52×A4)
unambiguous semidirect product(C5×C109)⋊(C5×A4)

Splittings

Fitting, socle, HallC22×C52×C109 ⋊ C3
derived, HallC22×C109 ⋊ C3×C52
HallC52×C109 ⋊ A4
SylowC109 ⋊ C52×A4
HallC22×C52 ⋊ C109⋊C3
SylowC22 ⋊ C52×C109⋊C3

Subgroups

subgroupG/H
center, hypercenterC52C22⋊(C109⋊C3)
commutator, cosocle, hypocenterC22×C109C3×C52
FrattiniC1G
Fitting, socleC22×C52×C109C3
LCSG ▷ C22×C109
UCSC1 ◁ C52

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10900

Conjugacy classes & character table

3700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32700, 202);