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C2×C3⋊(C5⋊D385) #37528759

order23100
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C3⋊(C5⋊D385)
unambiguous semidirect product(C2×C3)⋊(C5⋊D385)
unambiguous semidirect product(C2×C5)⋊D1155
unambiguous semidirect product(C2×C7)⋊(C3⋊(C5⋊D55))
unambiguous semidirect product(C2×C11)⋊(C3⋊(C5⋊D35))

Splittings

Fitting, socleC2×C3×C52×C7×C11 ⋊ C2
derived, HallC3×C52×C7×C11 ⋊ C22
HallC52×C7×C11 ⋊ C2×D3
HallC3×C52×C11 ⋊ C2×D7
HallC3×C52×C7 ⋊ C2×D11
HallC52×C11 ⋊ C2×D21
HallC3×C7×C11 ⋊ C2×C5⋊D5
HallC52×C7 ⋊ C2×D33
HallC7×C11 ⋊ C2×C3⋊(C5⋊D5)
HallC3×C52 ⋊ C2×D77
HallC3×C11 ⋊ C2×C5⋊D35
SylowC52 ⋊ C2×D231
HallC3×C7 ⋊ C2×C5⋊D55
SylowC11 ⋊ C2×C3⋊(C5⋊D35)
SylowC7 ⋊ C2×C3⋊(C5⋊D55)
SylowC3 ⋊ C2×C5⋊D385

Subgroups

subgroupG/H
center, hypercenterC2C3⋊(C5⋊D385)
commutator, cosocle, hypocenterC3×C52×C7×C11C22
FrattiniC1G
Fitting, socleC2×C3×C52×C7×C11C2
LCSG ▷ C3×C52×C7×C11
UCSC1 ◁ C2

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11550

Conjugacy classes & character table

5778 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 570);