Finite Group Databasebeta

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C3×C5×ΓL(1,𝔽8)×C103 #44570071

order32445
automorphism?
homologyAbelianization (H1) = C32×C5×C103 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×ΓL(1,𝔽8)×C103
unambiguous semidirect productC7⋊(C32×C5×C103)
unambiguous semidirect product(C3×C7)⋊(C3×C5×C103)
unambiguous semidirect product(C5×C7)⋊(C32×C103)
unambiguous semidirect product(C3×C5×C7)⋊(C3×C103)

Splittings

Fitting, socleC3×C5×C7×C103 ⋊ C3
derived, SylowC7 ⋊ C32×C5×C103
HallC5×C7×C103 ⋊ C32
HallC7×C103 ⋊ C32×C5
HallC5×C7 ⋊ C32×C103

Subgroups

subgroupG/H
center, hypercenterC3×C5×C103ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C32×C5×C103
FrattiniC1G
Fitting, socleC3×C5×C7×C103C3
LCSG ▷ C7
UCSC1 ◁ C3×C5×C103

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10815

Conjugacy classes & character table

7725 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32445, 9);