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C2×C5×C7×D213 #44447282

order29820
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×D213
unambiguous semidirect product(C2×C3)⋊(C5×C7×D71)

Splittings

Fitting, socleC2×C3×C5×C7×C71 ⋊ C2
derived, HallC3×C71 ⋊ C22×C5×C7
HallC3×C5×C7×C71 ⋊ C22
HallC5×C7×C71 ⋊ C2×D3
HallC3×C7×C71 ⋊ C22×C5
HallC3×C5×C71 ⋊ C22×C7
HallC7×C71 ⋊ C2×C5×D3
HallC5×C71 ⋊ C2×D3×C7
HallC3×C5×C7 ⋊ C2×D71
SylowC71 ⋊ C2×C5×D3×C7
HallC3×C7 ⋊ C2×C5×D71
HallC3×C5 ⋊ C2×C7×D71
SylowC3 ⋊ C2×C5×C7×D71

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D213
commutator, cosocle, hypocenterC3×C71C22×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C71C2
LCSG ▷ C3×C71
UCSC1 ◁ C2×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14910

Conjugacy classes & character table

7560 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29820, 170);