Finite Group Databasebeta

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C4×C5×C211⋊C7 #44443442

order29540
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×C211⋊C7
unambiguous semidirect product(C4×C5×C211)⋊C7

Splittings

Fitting, HallC4×C5×C211 ⋊ C7
derived, SylowC211 ⋊ C4×C5×C7
HallC5×C211 ⋊ C4×C7
HallC4×C211 ⋊ C5×C7

Subgroups

subgroupG/H
center, hypercenterC4×C5C211⋊C7
commutator, hypocenterC211C4×C5×C7
FrattiniC2C2×C5×C211⋊C7
FittingC4×C5×C211C7
socleC2×C5×C211C2×C7
prime radicalC2×C5×C211⋊C7C2
cosocleC2×C211C2×C5×C7
LCSG ▷ C211
UCSC1 ◁ C4×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4220

Conjugacy classes & character table

740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29540, 2);