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C2×#10620252⋊C25 #45654374

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

Aliases

direct productC2×#10620252⋊C25
unambiguous semidirect product(C2×#10620252)⋊C25

Splittings

derived, HallC7×C31 ⋊ C2×C3×C25
HallC2×C7×C31⋊C25 ⋊ C3
HallC7×C31⋊C25 ⋊ C2×C3
HallC2×C31⋊C25 ⋊ ΓL(1,𝔽8)
HallC2×#10620252 ⋊ C25
HallC31⋊C25 ⋊ C2×ΓL(1,𝔽8)
Hall#10620252 ⋊ C2×C25
HallC2×C7×C31 ⋊ C3×C25
HallC2×C31 ⋊ ΓL(1,𝔽8)×C25
SylowC31 ⋊ C2×ΓL(1,𝔽8)×C25
HallC2×C7 ⋊ (C31⋊C3)⋊C25
SylowC7 ⋊ C2×(C31⋊C3)⋊C25

Subgroups

subgroupG/H
center, hypercenterC2×C5#10620252⋊C5
commutator, hypocenterC7×C31C2×C3×C25
FrattiniC5C2×#10620252⋊C5
Fitting, socleC2×C5×C7×C31C3×C5
prime radicalC2×C5×#10620252C5
cosocleC5×C7×C31C2×C3×C5
LCSG ▷ C7×C31
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10850

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32550, 10);