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C2×C7×C3⋊(C5⋊D55) #37528757

order23100
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C7×C3⋊(C5⋊D55)
unambiguous semidirect product(C2×C3)⋊(C7×C5⋊D55)
unambiguous semidirect product(C2×C5)⋊(C7×D165)
unambiguous semidirect product(C2×C11)⋊(C7×C3⋊(C5⋊D5))

Splittings

Fitting, socleC2×C3×C52×C7×C11 ⋊ C2
derived, HallC3×C52×C11 ⋊ C22×C7
HallC3×C52×C7×C11 ⋊ C22
HallC52×C7×C11 ⋊ C2×D3
HallC3×C52×C7 ⋊ C2×D11
HallC52×C11 ⋊ C2×D3×C7
HallC3×C7×C11 ⋊ C2×C5⋊D5
HallC52×C7 ⋊ C2×D33
HallC7×C11 ⋊ C2×C3⋊(C5⋊D5)
HallC3×C52 ⋊ C2×C7×D11
HallC3×C11 ⋊ C2×C7×C5⋊D5
SylowC52 ⋊ C2×C7×D33
HallC3×C7 ⋊ C2×C5⋊D55
SylowC11 ⋊ C2×C7×C3⋊(C5⋊D5)
SylowC3 ⋊ C2×C7×C5⋊D55

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(C5⋊D55)
commutator, cosocle, hypocenterC3×C52×C11C22×C7
FrattiniC1G
Fitting, socleC2×C3×C52×C7×C11C2
LCSG ▷ C3×C52×C11
UCSC1 ◁ C2×C7

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 33
transitive degreeμt(G) = 11550

A minimal faithful permutation representation — 3 generators on 33 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(13,14)(15,16,17,18,19,20,21)(23,24)(25,26)(28,29)(30,31);(1,2,4,6,8,10,11,9,7,5,3)(12,13,14)(27,28,30,31,29)(32,33);(22,23,25,26,24)

Conjugacy classes & character table

5796 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 568);