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C5×(D211⋊C3)⋊C7 #56004681

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

Aliases

direct productC5×(D211⋊C3)⋊C7

Splittings

Fitting, socle, HallC5×C211 ⋊ C2×C3×C7
derived, SylowC211 ⋊ C2×C3×C5×C7
HallC5×(C211⋊C3)⋊C7 ⋊ C2
HallC5×D211⋊C7 ⋊ C3
HallC5×C211⋊C7 ⋊ C2×C3
HallC5×D211⋊C3 ⋊ C7
Hall(C211⋊C3)⋊C7 ⋊ C2×C5
HallC5×C211⋊C3 ⋊ C2×C7
HallD211⋊C7 ⋊ C3×C5
HallC5×D211 ⋊ C3×C7
HallC211⋊C7 ⋊ C2×C3×C5
HallD211⋊C3 ⋊ C5×C7
HallC211⋊C3 ⋊ C2×C5×C7
HallD211 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC5(D211⋊C3)⋊C7
commutator, cosocle, hypocenterC211C2×C3×C5×C7
FrattiniC1G
Fitting, socleC5×C211C2×C3×C7
LCSG ▷ C211
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

235 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(44310, 75);