Finite Group Databasebeta

← Prev (#56004655) Next (#56004657) →

C5×#22579724 #56004656

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

Aliases

direct productC5×#22579724

Splittings

Fitting, socle, HallC5×C7×C211 ⋊ C2×C3
derived, HallC7×C211 ⋊ C2×C3×C5
HallC5×#17984521 ⋊ C2
HallC5×C7×D211 ⋊ C3
Hall#17984521 ⋊ C2×C5
HallC7×D211 ⋊ C3×C5
HallC5×D211 ⋊ ΓL(1,𝔽8)
HallC5×C211 ⋊ C2×ΓL(1,𝔽8)
HallD211 ⋊ C5×ΓL(1,𝔽8)
SylowC211 ⋊ C2×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ D211⋊C3
SylowC7 ⋊ C5×D211⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#22579724
commutator, cosocle, hypocenterC7×C211C2×C3×C5
FrattiniC1G
Fitting, socleC5×C7×C211C2×C3
LCSG ▷ C7×C211
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1275 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(44310, 50);