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C2×C11×C3⋊(C5⋊D35) #37528758

order23100
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C11×C3⋊(C5⋊D35)
unambiguous semidirect product(C2×C3)⋊(C11×C5⋊D35)
unambiguous semidirect product(C2×C5)⋊(C11×D105)
unambiguous semidirect product(C2×C7)⋊(C11×C3⋊(C5⋊D5))

Splittings

Fitting, socleC2×C3×C52×C7×C11 ⋊ C2
derived, HallC3×C52×C7 ⋊ C22×C11
HallC3×C52×C7×C11 ⋊ C22
HallC52×C7×C11 ⋊ C2×D3
HallC3×C52×C11 ⋊ C2×D7
HallC52×C11 ⋊ C2×D21
HallC3×C7×C11 ⋊ C2×C5⋊D5
HallC52×C7 ⋊ C2×D3×C11
HallC7×C11 ⋊ C2×C3⋊(C5⋊D5)
HallC3×C52 ⋊ C2×C11×D7
HallC3×C11 ⋊ C2×C5⋊D35
SylowC52 ⋊ C2×C11×D21
HallC3×C7 ⋊ C2×C11×C5⋊D5
SylowC7 ⋊ C2×C11×C3⋊(C5⋊D5)
SylowC3 ⋊ C2×C11×C5⋊D35

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊(C5⋊D35)
commutator, cosocle, hypocenterC3×C52×C7C22×C11
FrattiniC1G
Fitting, socleC2×C3×C52×C7×C11C2
LCSG ▷ C3×C52×C7
UCSC1 ◁ C2×C11

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

Conjugacy classes & character table

5808 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 569);