Finite Group Databasebeta

← Prev (#44570068) Next (#44570070) →

C5×ΓL(1,𝔽8)×C103⋊C3 #44570069

order32445
automorphism?
homologyAbelianization (H1) = C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC5×ΓL(1,𝔽8)×C103⋊C3
unambiguous semidirect product(ΓL(1,𝔽8)×C103)⋊(C3×C5)
unambiguous semidirect product(C7×C103⋊C3)⋊(C3×C5)
unambiguous semidirect product#14524189⋊(C3×C5)
unambiguous semidirect product#14524190⋊(C3×C5)
unambiguous semidirect product(C5×C7×C103⋊C3)⋊C3
unambiguous semidirect product(C5×ΓL(1,𝔽8)×C103)⋊C3
unambiguous semidirect product(C5×#14524190)⋊C3
unambiguous semidirect product(C5×#14524189)⋊C3

Splittings

Fitting, socle, HallC5×C7×C103 ⋊ C32
derived, HallC7×C103 ⋊ C32×C5
HallC5×C103 ⋊ C3×ΓL(1,𝔽8)
SylowC103 ⋊ C3×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C3×C103⋊C3
SylowC7 ⋊ C3×C5×C103⋊C3

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×C103⋊C3
commutator, cosocle, hypocenterC7×C103C32×C5
FrattiniC1G
Fitting, socleC5×C7×C103C32
LCSG ▷ C7×C103
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3605

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32445, 7);