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D15×C211⋊C7 #56004641

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

Aliases

direct productD15×C211⋊C7

Splittings

Fitting, socle, derived, HallC3×C5×C211 ⋊ C2×C7
HallC3×C5×C211⋊C7 ⋊ C2
HallC5×C211⋊C7 ⋊ D3
HallD15×C211 ⋊ C7
HallC3×C211⋊C7 ⋊ D5
HallC5×C211 ⋊ D3×C7
HallC3×C211 ⋊ C7×D5
SylowC211 ⋊ C7×D15
HallC3×C5 ⋊ C2×C211⋊C7
SylowC5 ⋊ D3×C211⋊C7
SylowC3 ⋊ D5×C211⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C211C2×C7
LCSG ▷ C3×C5×C211
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

333 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(44310, 35);