Finite Group Databasebeta

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C3×Dic1925 #37528200

order23100
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic1925
unambiguous semidirect productC11⋊(C3×Dic175)

Splittings

derived, HallC7×C11×C25 ⋊ C3×C4
HallC3×C7×C11×C25 ⋊ C4
HallC3×C11×C25 ⋊ Dic7
HallC3×C7×C25 ⋊ Dic11
HallC11×C25 ⋊ C3×Dic7
HallC3×C7×C11 ⋊ Dic25
HallC7×C25 ⋊ C3×Dic11
HallC7×C11 ⋊ C3×Dic25
HallC3×C25 ⋊ Dic77
HallC3×C11 ⋊ Dic175
SylowC25 ⋊ C3×Dic77
HallC3×C7 ⋊ Dic275
SylowC11 ⋊ C3×Dic175
SylowC7 ⋊ C3×Dic275

Subgroups

subgroupG/H
center, hypercenterC2×C3D1925
commutator, hypocenterC7×C11×C25C3×C4
FrattiniC2×C5C3×D385
FittingC2×C3×C7×C11×C25C2
socle, prime radicalC2×C3×C5×C7×C11D5
cosocleC2×C7×C11×C25C2×C3
LCSG ▷ C7×C11×C25
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Conjugacy classes & character table

5784 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 11);