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C3×C23×C22⋊(C52⋊C3) #35208236

order20700
automorphism?
homologyAbelianization (H1) = C32×C23 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC3×C23×C22⋊(C52⋊C3)
unambiguous semidirect product(C22×C3)⋊(C23×C52⋊C3)
unambiguous semidirect product(C3×C52)⋊(A4×C23)
unambiguous semidirect product(C22×C3×C23)⋊(C52⋊C3)
unambiguous semidirect product(C3×C52×C23)⋊A4

Splittings

Fitting, socleC22×C3×C52×C23 ⋊ C3
derived, HallC22×C52 ⋊ C32×C23
HallC22×C52×C23 ⋊ C32
HallC52×C23 ⋊ C3×A4
HallC22×C23 ⋊ C3×C52⋊C3
SylowC52 ⋊ C3×A4×C23
SylowC22 ⋊ C3×C23×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC3×C23C22⋊(C52⋊C3)
commutator, cosocle, hypocenterC22×C52C32×C23
FrattiniC1G
Fitting, socleC22×C3×C52×C23C3
LCSG ▷ C22×C52
UCSC1 ◁ C3×C23

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2070

Conjugacy classes & character table

2484 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20700, 352);