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ΓL(1,𝔽8)×C25×D31 #45654398

order32550
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×C25×D31

Splittings

Fitting, HallC7×C25×C31 ⋊ C2×C3
derived, HallC7×C31 ⋊ C2×C3×C25
HallΓL(1,𝔽8)×C25×C31 ⋊ C2
HallC7×C25×D31 ⋊ C3
HallC25×C31 ⋊ C2×ΓL(1,𝔽8)
HallΓL(1,𝔽8)×C31 ⋊ C2×C25
HallC7×D31 ⋊ C3×C25
HallC7×C25 ⋊ C3×D31
SylowC31 ⋊ C2×ΓL(1,𝔽8)×C25
SylowC7 ⋊ C3×C25×D31

Subgroups

subgroupG/H
center, hypercenterC25ΓL(1,𝔽8)×D31
commutator, hypocenterC7×C31C2×C3×C25
FrattiniC5C5×ΓL(1,𝔽8)×D31
FittingC7×C25×C31C2×C3
socle, cosocleC5×C7×C31C2×C3×C5
prime radicalC5×ΓL(1,𝔽8)×D31C5
LCSG ▷ C7×C31
UCSC1 ◁ C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5425

Conjugacy classes & character table

2125 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32550, 34);