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D5×(C211⋊C3)⋊C7 #56004682

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

Aliases

direct productD5×(C211⋊C3)⋊C7

Splittings

Fitting, socle, derived, HallC5×C211 ⋊ C2×C3×C7
HallC5×(C211⋊C3)⋊C7 ⋊ C2
HallD5×C211⋊C7 ⋊ C3
HallC5×C211⋊C7 ⋊ C2×C3
HallD5×C211⋊C3 ⋊ C7
HallC5×C211⋊C3 ⋊ C2×C7
HallD5×C211 ⋊ C3×C7
HallC211⋊C7 ⋊ C3×D5
HallC211⋊C3 ⋊ C7×D5
SylowC211 ⋊ C3×C7×D5
SylowC5 ⋊ C2×(C211⋊C3)⋊C7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C211C2×C3×C7
LCSG ▷ C5×C211
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

124 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(44310, 76);