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D3×C7×C211⋊C5 #56004646

order44310
automorphism?
homologyAbelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productD3×C7×C211⋊C5

Splittings

Fitting, socle, HallC3×C7×C211 ⋊ C2×C5
derived, HallC3×C211 ⋊ C2×C5×C7
HallC3×C7×C211⋊C5 ⋊ C2
HallD3×C7×C211 ⋊ C5
HallC3×C211⋊C5 ⋊ C2×C7
HallC7×C211 ⋊ C5×D3
HallD3×C211 ⋊ C5×C7
SylowC211 ⋊ C5×D3×C7
HallC3×C7 ⋊ C2×C211⋊C5
SylowC3 ⋊ C2×C7×C211⋊C5

Subgroups

subgroupG/H
center, hypercenterC7D3×C211⋊C5
commutator, cosocle, hypocenterC3×C211C2×C5×C7
FrattiniC1G
Fitting, socleC3×C7×C211C2×C5
LCSG ▷ C3×C211
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

987 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(44310, 40);