Finite Group Databasebeta

← Prev (#56004608) Next (#56004610) →

C2×C3×C7×C211⋊C5 #56004609

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

Aliases

direct productC2×C3×C7×C211⋊C5

Splittings

Fitting, socle, HallC2×C3×C7×C211 ⋊ C5
derived, SylowC211 ⋊ C2×C3×C5×C7
HallC3×C7×C211 ⋊ C2×C5
HallC2×C7×C211 ⋊ C3×C5
HallC7×C211 ⋊ C2×C3×C5
HallC2×C3×C211 ⋊ C5×C7
HallC3×C211 ⋊ C2×C5×C7
HallC2×C211 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7C211⋊C5
commutator, cosocle, hypocenterC211C2×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C7×C211C5
LCSG ▷ C211
UCSC1 ◁ C2×C3×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1974 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(44310, 3);