Finite Group Databasebeta

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C72×D5×C11⋊C5 #41003991

order26950
automorphism?
homologyAbelianization (H1) = C2×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productC72×D5×C11⋊C5
unambiguous semidirect productC5⋊(C2×C72×C11⋊C5)
unambiguous semidirect product(D5×C11)⋊(C5×C72)
unambiguous semidirect product(C7×D5×C11)⋊(C5×C7)
unambiguous semidirect product(C72×D5×C11)⋊C5

Splittings

Fitting, socleC5×C72×C11 ⋊ C2×C5
derivedC5×C11 ⋊ C2×C5×C72
HallC5×C72×C11⋊C5 ⋊ C2
HallC72×C11 ⋊ C5×D5
HallC5×C11⋊C5 ⋊ C2×C72
SylowC11 ⋊ C5×C72×D5

Subgroups

subgroupG/H
center, hypercenterC72D5×C11⋊C5
commutator, cosocle, hypocenterC5×C11C2×C5×C72
FrattiniC1G
Fitting, socleC5×C72×C11C2×C5
LCSG ▷ C5×C11
UCSC1 ◁ C72

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2695

Conjugacy classes & character table

1372 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26950, 58);