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C22×C11×C7⋊(C52⋊C3) #37528735

order23100
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2×C5

Aliases

direct productC22×C11×C7⋊(C52⋊C3)

Splittings

Fitting, socle, HallC22×C52×C7×C11 ⋊ C3
derived, HallC52×C7 ⋊ C22×C3×C11
HallC52×C7×C11 ⋊ C22×C3
HallC22×C52×C11 ⋊ ΓL(1,𝔽8)
HallC22×C52×C7 ⋊ C3×C11
HallC22×C7×C11 ⋊ C52⋊C3
HallC52×C11 ⋊ C22×ΓL(1,𝔽8)
HallC22×C52 ⋊ C11×ΓL(1,𝔽8)
HallC7×C11 ⋊ C22×C52⋊C3
HallC22×C7 ⋊ C11×C52⋊C3
SylowC52 ⋊ C22×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C22×C11×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC22×C11C7⋊(C52⋊C3)
commutator, cosocle, hypocenterC52×C7C22×C3×C11
FrattiniC1G
Fitting, socleC22×C52×C7×C11C3
LCSG ▷ C52×C7
UCSC1 ◁ C22×C11

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

2684 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 546);