Finite Group Databasebeta

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C3×C4×C7×C11⋊C25 #37528191

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C4×C7×C11⋊C25
unambiguous semidirect product(C4×C11)⋊(C3×C7×C25)
unambiguous semidirect product(C3×C4×C11)⋊(C7×C25)
unambiguous semidirect product(C3×C4×C7×C11)⋊C25

Splittings

derived, SylowC11 ⋊ C3×C4×C7×C25
HallC3×C4×C7×C11 ⋊ C25
HallC4×C7×C11 ⋊ C3×C25
HallC3×C7×C11 ⋊ C4×C25
HallC3×C4×C11 ⋊ C7×C25
HallC7×C11 ⋊ C3×C4×C25
HallC4×C11 ⋊ C3×C7×C25
HallC3×C11 ⋊ C4×C7×C25

Subgroups

subgroupG/H
center, hypercenterC3×C4×C5×C7C11⋊C5
commutator, hypocenterC11C3×C4×C7×C25
FrattiniC2×C5C2×C3×C7×C11⋊C5
FittingC3×C4×C5×C7×C11C5
socle, prime radicalC2×C3×C5×C7×C11C2×C5
cosocleC2×C5×C11C2×C3×C5×C7
LCSG ▷ C11
UCSC1 ◁ C3×C4×C5×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Conjugacy classes & character table

2940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 2);