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C2×C5×C11×D23 #19099460

order5060
isoclinismisoclinic class of D23
automorphism?
homologyAbelianization (H1) = C22×C5×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C11×D23

Splittings

Fitting, socleC2×C5×C11×C23 ⋊ C2
derived, SylowC23 ⋊ C22×C5×C11
HallC5×C11×C23 ⋊ C22
HallC11×C23 ⋊ C22×C5
HallC5×C23 ⋊ C22×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D23
commutator, hypocenterC23C22×C5×C11
FrattiniC1G
Fitting, socleC2×C5×C11×C23C2
LCSG ▷ C23
UCSC1 ◁ C2×C5×C11

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1430 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×C11×D23, C2×C5×C11×D69, C2×C3×C5×C11×D23, …
maximal normal subgroup ofC2×C3×C5×C11×D23, C2×D23×C11⋊C25, C2×C11×C25×D23, …
maximal quotient ofC5×D3×C11×D23, C2×C5×C11×D69, C2×C3×C5×C11×D23, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5060, 47);