Finite Group Databasebeta

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C5×C9×Dic149 #41001216

order26820
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×Dic149

Splittings

derived, SylowC149 ⋊ C4×C5×C9
HallC5×C9×C149 ⋊ C4
HallC9×C149 ⋊ C4×C5
HallC5×C149 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC2×C5×C9D149
commutator, hypocenterC149C4×C5×C9
FrattiniC2×C3C3×C5×D149
FittingC2×C5×C9×C149C2
socle, prime radicalC2×C3×C5×C149C2×C3
cosocleC2×C3×C149C2×C3×C5
LCSG ▷ C149
UCSC1 ◁ C2×C5×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26820

Conjugacy classes & character table

6840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26820, 2);