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C2×D23×C11⋊C5 #19099441

order5060
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×D23×C11⋊C5
unambiguous semidirect productC23⋊(C22×C11⋊C5)
unambiguous semidirect product(C2×C23)⋊(C2×C11⋊C5)
unambiguous semidirect product(C2×C11×D23)⋊C5

Splittings

Fitting, socleC2×C11×C23 ⋊ C2×C5
derived, HallC11×C23 ⋊ C22×C5
HallC23×C11⋊C5 ⋊ C22
HallC2×C11×D23 ⋊ C5
SylowC23 ⋊ C22×C11⋊C5
SylowC11 ⋊ C2×C5×D23

Subgroups

subgroupG/H
center, hypercenterC2D23×C11⋊C5
commutator, hypocenterC11×C23C22×C5
FrattiniC1G
Fitting, socleC2×C11×C23C2×C5
LCSG ▷ C11×C23
UCSC1 ◁ C2

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

182 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D23×C11⋊C5, C2×C3×D23×C11⋊C5, C2×C11⋊C5×D69, …
maximal normal subgroup ofC2×C3×D23×C11⋊C5, C2×C5×D23×C11⋊C5, C2×C7×D23×C11⋊C5
maximal quotient ofD3×D23×C11⋊C5, C2×C3×D23×C11⋊C5, C2×C11⋊C5×D69, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5060, 28);