Finite Group Databasebeta

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C3×C7×Dic23⋊C11 #36318342

order21252
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×Dic23⋊C11
unambiguous semidirect productDic23⋊(C3×C7×C11)
unambiguous semidirect product(C23⋊C11)⋊(C3×C4×C7)
unambiguous semidirect product(C3×Dic23)⋊(C7×C11)
unambiguous semidirect product(C3×C7×Dic23)⋊C11

Splittings

derived, SylowC23 ⋊ C3×C4×C7×C11
HallC3×C7×C23⋊C11 ⋊ C4
HallC3×C7×Dic23 ⋊ C11
HallC7×C23⋊C11 ⋊ C3×C4
HallC3×C23⋊C11 ⋊ C4×C7
HallC7×Dic23 ⋊ C3×C11
HallC3×C7×C23 ⋊ C4×C11
HallC3×Dic23 ⋊ C7×C11
HallC23⋊C11 ⋊ C3×C4×C7
HallC7×C23 ⋊ C3×C4×C11
HallDic23 ⋊ C3×C7×C11
HallC3×C23 ⋊ C4×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7AGL(1,𝔽23)
commutator, hypocenterC23C3×C4×C7×C11
FrattiniC2C3×C7×AGL(1,𝔽23)
Fitting, socleC2×C3×C7×C23C2×C11
prime radicalC2×C3×C7×C23⋊C11C2
cosocleC2×C23C2×C3×C7×C11
LCSG ▷ C23
UCSC1 ◁ C2×C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1932

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21252, 20);