Finite Group Databasebeta

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C3×C7×Dic275 #37528198

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×Dic275
unambiguous semidirect productC11⋊(C3×C7×Dic25)

Splittings

derived, HallC11×C25 ⋊ C3×C4×C7
HallC3×C7×C11×C25 ⋊ C4
HallC7×C11×C25 ⋊ C3×C4
HallC3×C11×C25 ⋊ C4×C7
HallC3×C7×C25 ⋊ Dic11
HallC3×C7×C11 ⋊ Dic25
HallC7×C25 ⋊ C3×Dic11
HallC7×C11 ⋊ C3×Dic25
HallC3×C25 ⋊ C7×Dic11
HallC3×C11 ⋊ C7×Dic25
SylowC25 ⋊ C3×C7×Dic11
SylowC11 ⋊ C3×C7×Dic25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D275
commutator, hypocenterC11×C25C3×C4×C7
FrattiniC2×C5C3×C7×D55
FittingC2×C3×C7×C11×C25C2
socle, prime radicalC2×C3×C5×C7×C11D5
cosocleC2×C11×C25C2×C3×C7
LCSG ▷ C11×C25
UCSC1 ◁ C2×C3×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Conjugacy classes & character table

5838 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 9);