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C7×(D211⋊C3)⋊C5 #56004684

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

Aliases

direct productC7×(D211⋊C3)⋊C5

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC7(D211⋊C3)⋊C5
commutator, cosocle, hypocenterC211C2×C3×C5×C7
FrattiniC1G
Fitting, socleC7×C211C2×C3×C5
LCSG ▷ C211
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

259 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(44310, 78);