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C5×Dic23⋊C11 #19099424

order5060
automorphism?
homologyAbelianization (H1) = C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic23⋊C11
unambiguous semidirect productDic23⋊(C5×C11)
unambiguous semidirect product(C23⋊C11)⋊(C4×C5)
unambiguous semidirect product(C5×Dic23)⋊C11

Splittings

derived, SylowC23 ⋊ C4×C5×C11
HallC5×C23⋊C11 ⋊ C4
HallC5×Dic23 ⋊ C11
HallC23⋊C11 ⋊ C4×C5
HallC5×C23 ⋊ C4×C11
HallDic23 ⋊ C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5AGL(1,𝔽23)
commutator, hypocenterC23C4×C5×C11
FrattiniC2C5×AGL(1,𝔽23)
Fitting, socleC2×C5×C23C2×C11
LCSG ▷ C23
UCSC1 ◁ C2×C5

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×Dic23⋊C11, C5×C3⋊(Dic23⋊C11), C25×Dic23⋊C11, …
maximal normal subgroup ofC3×C5×Dic23⋊C11, C25×Dic23⋊C11, C52×Dic23⋊C11, …
maximal quotient ofC3×C5×Dic23⋊C11, C5×C3⋊(Dic23⋊C11), C25×Dic23⋊C11, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5060, 11);