Finite Group Databasebeta

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C2×C7×(C31⋊C3)⋊C25 #45654371

order32550
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC2×C7×(C31⋊C3)⋊C25
unambiguous semidirect product(C2×C31⋊C3)⋊(C7×C25)
unambiguous semidirect product(C2×C7×C31⋊C3)⋊C25
unambiguous semidirect product(C2×C31⋊C25)⋊(C3×C7)

Splittings

derived, SylowC31 ⋊ C2×C3×C7×C25
HallC2×C7×C31⋊C25 ⋊ C3
HallC7×C31⋊C25 ⋊ C2×C3
HallC2×C31⋊C25 ⋊ C3×C7
HallC2×C7×C31⋊C3 ⋊ C25
HallC31⋊C25 ⋊ C2×C3×C7
HallC7×C31⋊C3 ⋊ C2×C25
HallC2×C7×C31 ⋊ C3×C25
HallC7×C31 ⋊ C2×C3×C25
HallC2×C31⋊C3 ⋊ C7×C25
HallC31⋊C3 ⋊ C2×C7×C25
HallC2×C31 ⋊ C3×C7×C25

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7(C31⋊C3)⋊C5
commutator, hypocenterC31C2×C3×C7×C25
FrattiniC5C2×C7×(C31⋊C3)⋊C5
Fitting, socleC2×C5×C7×C31C3×C5
prime radicalC2×C5×C7×C31⋊C3C5
cosocleC5×C31C2×C3×C5×C7
LCSG ▷ C31
UCSC1 ◁ C2×C5×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10850

Conjugacy classes & character table

1190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32550, 7);