Finite Group Databasebeta

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C7×C11×Dic3×C25 #37528201

order23100
automorphism?
homologyAbelianization (H1) = C4×C7×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×Dic3×C25
unambiguous semidirect productC3⋊(C4×C7×C11×C25)

Splittings

derived, SylowC3 ⋊ C4×C7×C11×C25
HallC3×C7×C11×C25 ⋊ C4
HallC3×C11×C25 ⋊ C4×C7
HallC3×C7×C25 ⋊ C4×C11
HallC3×C7×C11 ⋊ C4×C25
HallC3×C25 ⋊ C4×C7×C11
HallC3×C11 ⋊ C4×C7×C25
HallC3×C7 ⋊ C4×C11×C25

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11×C25D3
commutator, hypocenterC3C4×C7×C11×C25
FrattiniC2×C5C5×D3×C7×C11
FittingC2×C3×C7×C11×C25C2
socle, prime radicalC2×C3×C5×C7×C11C2×C5
cosocleC2×C3×C5C2×C5×C7×C11
LCSG ▷ C3
UCSC1 ◁ C2×C7×C11×C25

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Conjugacy classes & character table

11550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 12);