Finite Group Databasebeta

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C32×C5×C7×D23 #28408073

order14490
isoclinismisoclinic class of D23
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C7 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×C7×D23
unambiguous semidirect productC23⋊(C2×C32×C5×C7)

Splittings

Fitting, socle, HallC32×C5×C7×C23 ⋊ C2
derived, SylowC23 ⋊ C2×C32×C5×C7
HallC32×C7×C23 ⋊ C2×C5
HallC32×C5×C23 ⋊ C2×C7
HallC5×C7×C23 ⋊ C2×C32
HallC32×C23 ⋊ C2×C5×C7
HallC7×C23 ⋊ C2×C32×C5
HallC5×C23 ⋊ C2×C32×C7

Subgroups

subgroupG/H
center, hypercenterC32×C5×C7D23
commutator, cosocle, hypocenterC23C2×C32×C5×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C23C2
LCSG ▷ C23
UCSC1 ◁ C32×C5×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7245

Conjugacy classes & character table

4095 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C5×D7×D23, C32×C7×D5×D23, C32×D23×D35, …
maximal normal subgroup ofC32×C5×D7×D23, C32×C7×D5×D23, C32×D23×D35, …
maximal quotient ofC32×C5×C7×Dic23, C2×C32×C5×C7×D23

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14490, 64);