Finite Group Databasebeta

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C7×Dic3×C11⋊C25 #37528212

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

Aliases

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

Splittings

derived, HallC3×C11 ⋊ C4×C7×C25
HallC3×C7×C11⋊C25 ⋊ C4
HallC7×C11×Dic3 ⋊ C25
HallC3×C11⋊C25 ⋊ C4×C7
HallC3×C7×C11 ⋊ C4×C25
HallC11×Dic3 ⋊ C7×C25
HallC7×C11 ⋊ Dic3×C25
HallC3×C7 ⋊ C4×C11⋊C25
SylowC11 ⋊ C7×Dic3×C25
SylowC3 ⋊ C4×C7×C11⋊C25

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7D3×C11⋊C5
commutator, hypocenterC3×C11C4×C7×C25
FrattiniC2×C5D3×C7×C11⋊C5
Fitting, socle, prime radicalC2×C3×C5×C7×C11C2×C5
cosocleC2×C3×C5×C11C2×C5×C7
LCSG ▷ C3×C11
UCSC1 ◁ C2×C5×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Conjugacy classes & character table

1470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 23);