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C5×C7×(C43⋊C3)⋊C4 #31825354

order18060
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7×(C43⋊C3)⋊C4

Splittings

derived, SylowC43 ⋊ C3×C4×C5×C7
HallC5×C7×Dic43 ⋊ C3
HallC5×C7×C43⋊C3 ⋊ C4
HallC5×C7×C43 ⋊ C3×C4
HallC7×Dic43 ⋊ C3×C5
HallC7×C43⋊C3 ⋊ C4×C5
HallC5×Dic43 ⋊ C3×C7
HallC5×C43⋊C3 ⋊ C4×C7
HallC7×C43 ⋊ C3×C4×C5
HallC5×C43 ⋊ C3×C4×C7
HallDic43 ⋊ C3×C5×C7
HallC43⋊C3 ⋊ C4×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D43⋊C3
commutator, hypocenterC43C3×C4×C5×C7
FrattiniC2C5×C7×D43⋊C3
Fitting, socleC2×C5×C7×C43C2×C3
prime radicalC2×C5×C7×C43⋊C3C2
cosocleC2×C43C2×C3×C5×C7
LCSG ▷ C43
UCSC1 ◁ C2×C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6020

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18060, 30);