Finite Group Databasebeta

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C3×C7×C11×#1044 #37528634

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C11 · Schur multiplier (H2) = C5

Aliases

direct productC3×C7×C11×#1044

Splittings

Fitting, socle, HallC3×C52×C7×C11 ⋊ C4
derived, SylowC52 ⋊ C3×C4×C7×C11
HallC52×C7×C11 ⋊ C3×C4
HallC3×C52×C11 ⋊ C4×C7
HallC3×C52×C7 ⋊ C4×C11
HallC52×C11 ⋊ C3×C4×C7
HallC52×C7 ⋊ C3×C4×C11
HallC3×C52 ⋊ C4×C7×C11

Subgroups

subgroupG/H
center, hypercenterC3×C7×C11#1044
commutator, hypocenterC52C3×C4×C7×C11
FrattiniC1G
Fitting, socleC3×C52×C7×C11C4
prime radicalC3×C7×C11×C5⋊D5C2
cosocleC5⋊D5C2×C3×C7×C11
LCSG ▷ C52
UCSC1 ◁ C3×C7×C11

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

2310 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 445);