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C2×C5×(C71⋊C5)⋊C7 #38733100

order24850
automorphism?
homologyAbelianization (H1) = C2×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC2×C5×(C71⋊C5)⋊C7
unambiguous semidirect product(C2×C71⋊C5)⋊(C5×C7)
unambiguous semidirect product(C2×C71⋊C7)⋊C52
unambiguous semidirect product(C2×C5×C71⋊C5)⋊C7
unambiguous semidirect product(C2×C5×C71⋊C7)⋊C5

Splittings

Fitting, socleC2×C5×C71 ⋊ C5×C7
derived, SylowC71 ⋊ C2×C52×C7
HallC2×C5×C71⋊C5 ⋊ C7
HallC5×C71⋊C5 ⋊ C2×C7
HallC2×C71⋊C7 ⋊ C52
HallC71⋊C7 ⋊ C2×C52
HallC2×C71 ⋊ C52×C7

Subgroups

subgroupG/H
center, hypercenterC2×C5(C71⋊C5)⋊C7
commutator, cosocle, hypocenterC71C2×C52×C7
FrattiniC1G
Fitting, socleC2×C5×C71C5×C7
LCSG ▷ C71
UCSC1 ◁ C2×C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 710

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24850, 23);