Finite Group Databasebeta

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C2×C3×D23×C52⋊C3 #35208124

order20700
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC2×C3×D23×C52⋊C3
unambiguous semidirect productC23⋊(C22×C3×C52⋊C3)
unambiguous semidirect product(C2×C23)⋊(C2×C3×C52⋊C3)
unambiguous semidirect product(C2×C52×D23)⋊C32
unambiguous semidirect product(C2×C3×C52×D23)⋊C3

Splittings

Fitting, socleC2×C3×C52×C23 ⋊ C2×C3
derived, HallC52×C23 ⋊ C22×C32
HallC3×C23×C52⋊C3 ⋊ C22
HallC2×C52×D23 ⋊ C32
SylowC52 ⋊ C2×C32×D23
SylowC23 ⋊ C22×C3×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3D23×C52⋊C3
commutator, cosocle, hypocenterC52×C23C22×C32
FrattiniC1G
Fitting, socleC2×C3×C52×C23C2×C3
LCSG ▷ C52×C23
UCSC1 ◁ C2×C3

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2070

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20700, 240);