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C11⋊C5×C127 #20296134

order6985
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C5×C127 · Schur multiplier (H2) = C1

Aliases

direct productC11⋊C5×C127
unambiguous semidirect productC11⋊(C5×C127)
unambiguous semidirect product(C11×C127)⋊C5

Splittings

Fitting, socle, HallC11×C127 ⋊ C5
derived, SylowC11 ⋊ C5×C127

Subgroups

subgroupG/H
center, hypercenterC127C11⋊C5
commutator, hypocenterC11C5×C127
FrattiniC1G
Fitting, socleC11×C127C5
LCSG ▷ C11
UCSC1 ◁ C127

8 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

889 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C11⋊C5×C127, C11⋊C5×D127, AGL(1,𝔽11)×C127, …
maximal normal subgroup ofC2×C11⋊C5×C127, C11⋊C5×D127, AGL(1,𝔽11)×C127, …
maximal quotient ofC2×C11⋊C5×C127, C3×C11⋊C5×C127, C127×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6985, 1);