Finite Group Databasebeta

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C3×C11×D7×D23 #36318397

order21252
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC3×C11×D7×D23

Splittings

Fitting, socle, HallC3×C7×C11×C23 ⋊ C22
derived, HallC7×C23 ⋊ C22×C3×C11
HallC7×C11×C23 ⋊ C22×C3
HallC3×C11×C23 ⋊ C2×D7
HallC3×C7×C23 ⋊ C22×C11
HallC11×C23 ⋊ C2×C3×D7
HallC3×C7×C11 ⋊ C2×D23
HallC7×C11 ⋊ C2×C3×D23
HallC3×C23 ⋊ C2×C11×D7
SylowC23 ⋊ C2×C3×C11×D7
HallC3×C7 ⋊ C2×C11×D23
SylowC7 ⋊ C2×C3×C11×D23

Subgroups

subgroupG/H
center, hypercenterC3×C11D7×D23
commutator, cosocle, hypocenterC7×C23C22×C3×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C23C22
LCSG ▷ C7×C23
UCSC1 ◁ C3×C11

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5313

Conjugacy classes & character table

2145 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21252, 75);