Finite Group Databasebeta

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C2×C3×C11×D175 #37528318

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C11×D175
unambiguous semidirect product(C2×C25)⋊(C3×C11×D7)

Splittings

FittingC2×C3×C7×C11×C25 ⋊ C2
derived, HallC7×C25 ⋊ C22×C3×C11
HallC3×C7×C11×C25 ⋊ C22
HallC7×C11×C25 ⋊ C22×C3
HallC3×C11×C25 ⋊ C2×D7
HallC3×C7×C25 ⋊ C22×C11
HallC11×C25 ⋊ C2×C3×D7
HallC3×C7×C11 ⋊ C2×D25
HallC7×C11 ⋊ C2×C3×D25
HallC3×C25 ⋊ C2×C11×D7
SylowC25 ⋊ C2×C3×C11×D7
HallC3×C7 ⋊ C2×C11×D25
SylowC7 ⋊ C2×C3×C11×D25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11D175
commutator, cosocle, hypocenterC7×C25C22×C3×C11
FrattiniC5C2×C3×C11×D35
FittingC2×C3×C7×C11×C25C2
socleC2×C3×C5×C7×C11D5
LCSG ▷ C7×C25
UCSC1 ◁ C2×C3×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11550

Conjugacy classes & character table

5874 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 129);