Finite Group Databasebeta

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C23×#13109900 #49179152

order37674
automorphism?
homologyAbelianization (H1) = C2×C9×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×#13109900

Splittings

derived, HallC7×C13 ⋊ C2×C9×C23
HallC23×#11717941 ⋊ C2
HallC13×D7×C23 ⋊ C9
HallC7×C13×C23 ⋊ C2×C9
Hall#11717941 ⋊ C2×C23
HallD7×C23 ⋊ C13⋊C9
HallC13×C23 ⋊ D7⋊C9
HallC13×D7 ⋊ C9×C23
HallC7×C23 ⋊ C2×C13⋊C9
HallD7 ⋊ C23×C13⋊C9
SylowC13 ⋊ C23×D7⋊C9
SylowC7 ⋊ C2×C23×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C23#10587720
commutator, hypocenterC7×C13C2×C9×C23
FrattiniC3C23×#10587720
Fitting, socleC3×C7×C13×C23C2×C3
prime radicalC3×C13×D7×C23C3
cosocleC3×C7×C13C2×C3×C23
LCSG ▷ C7×C13
UCSC1 ◁ C3×C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18837

Conjugacy classes & character table

1863 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37674, 35);