Finite Group Databasebeta

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C2×C5×C72×C11⋊C5 #41003996

order26950
automorphism?
homologyAbelianization (H1) = C2×C52×C72 · Schur multiplier (H2) = C5×C7

Aliases

direct productC2×C5×C72×C11⋊C5
unambiguous semidirect product(C2×C11)⋊(C52×C72)
unambiguous semidirect product(C2×C5×C11)⋊(C5×C72)
unambiguous semidirect product(C2×C7×C11)⋊(C52×C7)
unambiguous semidirect product(C2×C5×C7×C11)⋊(C5×C7)
unambiguous semidirect product(C2×C72×C11)⋊C52
unambiguous semidirect product(C2×C5×C72×C11)⋊C5

Splittings

Fitting, socleC2×C5×C72×C11 ⋊ C5
derived, SylowC11 ⋊ C2×C52×C72
HallC2×C72×C11 ⋊ C52
HallC72×C11 ⋊ C2×C52
HallC2×C11 ⋊ C52×C72

Subgroups

subgroupG/H
center, hypercenterC2×C5×C72C11⋊C5
commutator, cosocle, hypocenterC11C2×C52×C72
FrattiniC1G
Fitting, socleC2×C5×C72×C11C5
LCSG ▷ C11
UCSC1 ◁ C2×C5×C72

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5390

Conjugacy classes & character table

3430 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26950, 63);