Finite Group Databasebeta

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C2×C3×C5×C7×D23 #23751658

order9660
isoclinismisoclinic class of D23
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×C7×D23
unambiguous semidirect productC23⋊(C22×C3×C5×C7)
unambiguous semidirect product(C2×C23)⋊(C2×C3×C5×C7)

Splittings

Fitting, socleC2×C3×C5×C7×C23 ⋊ C2
derived, SylowC23 ⋊ C22×C3×C5×C7
HallC3×C5×C7×C23 ⋊ C22
HallC5×C7×C23 ⋊ C22×C3
HallC3×C7×C23 ⋊ C22×C5
HallC3×C5×C23 ⋊ C22×C7
HallC7×C23 ⋊ C22×C3×C5
HallC5×C23 ⋊ C22×C3×C7
HallC3×C23 ⋊ C22×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C7D23
commutator, cosocle, hypocenterC23C22×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C23C2
LCSG ▷ C23
UCSC1 ◁ C2×C3×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2730 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×D23×C7⋊C9, C2×C5×C7×C9×D23, C2×C3×C5×ΓL(1,𝔽8)×D23, …
maximal normal subgroup ofC2×C5×D23×C7⋊C9, C2×C5×C7×C9×D23, C2×C3×C5×ΓL(1,𝔽8)×D23, …
maximal quotient ofC2×C5×C7×C9×D23, C3×C5×D3×C7×D23, C2×C32×C5×C7×D23, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9660, 104);