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C3×C7⋊(C23⋊AGL(1,𝔽5)) #23751602

order9660
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7⋊(C23⋊AGL(1,𝔽5))
unambiguous semidirect productC23⋊(C3×C7⋊AGL(1,𝔽5))

Splittings

Fitting, socle, HallC3×C5×C7×C23 ⋊ C4
derived, HallC5×C7×C23 ⋊ C3×C4
HallC3×C7×C23 ⋊ AGL(1,𝔽5)
HallC3×C5×C23 ⋊ Dic7
HallC7×C23 ⋊ C3×AGL(1,𝔽5)
HallC5×C23 ⋊ C3×Dic7
HallC3×C5×C7 ⋊ Dic23
HallC3×C23 ⋊ C7⋊AGL(1,𝔽5)
HallC5×C7 ⋊ C3×Dic23
SylowC23 ⋊ C3×C7⋊AGL(1,𝔽5)
HallC3×C7 ⋊ C23⋊AGL(1,𝔽5)
HallC3×C5 ⋊ Dic161
SylowC7 ⋊ C3×C23⋊AGL(1,𝔽5)
SylowC5 ⋊ C3×Dic161

Subgroups

subgroupG/H
center, hypercenterC3C7⋊(C23⋊AGL(1,𝔽5))
commutator, hypocenterC5×C7×C23C3×C4
FrattiniC1G
Fitting, socleC3×C5×C7×C23C4
prime radicalC3×C7×D5×C23C2
cosocleC7×D5×C23C2×C3
LCSG ▷ C5×C7×C23
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

975 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC23⋊((C7⋊C9)⋊AGL(1,𝔽5)), C9×C7⋊(C23⋊AGL(1,𝔽5)), C3×ΓL(1,𝔽8)⋊(C23⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC23⋊((C7⋊C9)⋊AGL(1,𝔽5)), C9×C7⋊(C23⋊AGL(1,𝔽5)), C3×ΓL(1,𝔽8)⋊(C23⋊AGL(1,𝔽5)), …
maximal quotient ofC9×C7⋊(C23⋊AGL(1,𝔽5)), C32×C7⋊(C23⋊AGL(1,𝔽5)), C3×C3⋊(C7⋊(C23⋊AGL(1,𝔽5)))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9660, 48);