Finite Group Databasebeta

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C52×C7×C11×A4 #37528732

order23100
automorphism?
homologyAbelianization (H1) = C3×C52×C7×C11 · Schur multiplier (H2) = C2×C5

Aliases

direct productC52×C7×C11×A4
unambiguous semidirect productC22⋊(C3×C52×C7×C11)
unambiguous semidirect product(C22×C5)⋊(C3×C5×C7×C11)

Splittings

Fitting, socle, HallC22×C52×C7×C11 ⋊ C3
derived, SylowC22 ⋊ C3×C52×C7×C11
HallC22×C52×C11 ⋊ C3×C7
HallC22×C52×C7 ⋊ C3×C11
HallC22×C7×C11 ⋊ C3×C52
HallC22×C52 ⋊ C3×C7×C11
HallC22×C11 ⋊ C3×C52×C7
HallC22×C7 ⋊ C3×C52×C11

Subgroups

subgroupG/H
center, hypercenterC52×C7×C11A4
commutator, cosocle, hypocenterC22C3×C52×C7×C11
FrattiniC1G
Fitting, socleC22×C52×C7×C11C3
LCSG ▷ C22
UCSC1 ◁ C52×C7×C11

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7700

Conjugacy classes & character table

7700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 543);