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ΓL(1,𝔽8)×C25×C61 #44545048

order32025
automorphism?
homologyAbelianization (H1) = C3×C25×C61 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C25×C61
unambiguous semidirect productC7⋊(C3×C25×C61)
unambiguous semidirect product(C7×C25)⋊(C3×C61)

Splittings

Fitting, HallC7×C25×C61 ⋊ C3
derived, SylowC7 ⋊ C3×C25×C61
HallC7×C61 ⋊ C3×C25
HallC7×C25 ⋊ C3×C61

Subgroups

subgroupG/H
center, hypercenterC25×C61ΓL(1,𝔽8)
commutator, hypocenterC7C3×C25×C61
FrattiniC5C5×ΓL(1,𝔽8)×C61
FittingC7×C25×C61C3
socleC5×C7×C61C3×C5
prime radicalC5×ΓL(1,𝔽8)×C61C5
cosocleC5×C7C3×C5×C61
LCSG ▷ C7
UCSC1 ◁ C25×C61

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10675

Conjugacy classes & character table

7625 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32025, 4);