Finite Group Databasebeta

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C3×C7×D211⋊C5 #56004643

order44310
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×D211⋊C5

Splittings

Fitting, socle, HallC3×C7×C211 ⋊ C2×C5
derived, SylowC211 ⋊ C2×C3×C5×C7
HallC3×C7×C211⋊C5 ⋊ C2
HallC3×C7×D211 ⋊ C5
HallC7×C211⋊C5 ⋊ C2×C3
HallC3×C211⋊C5 ⋊ C2×C7
HallC7×D211 ⋊ C3×C5
HallC7×C211 ⋊ C2×C3×C5
HallC3×D211 ⋊ C5×C7
HallC211⋊C5 ⋊ C2×C3×C7
HallC3×C211 ⋊ C2×C5×C7
HallD211 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC3×C7D211⋊C5
commutator, cosocle, hypocenterC211C2×C3×C5×C7
FrattiniC1G
Fitting, socleC3×C7×C211C2×C5
LCSG ▷ C211
UCSC1 ◁ C3×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

651 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(44310, 37);