Finite Group Databasebeta

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C7×C11×C3⋊#1043 #37528722

order23100
automorphism?
homologyAbelianization (H1) = C4×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×C3⋊#1043
unambiguous semidirect productC3⋊(C7×C11×#1043)

Splittings

Fitting, socle, HallC3×C52×C7×C11 ⋊ C4
derived, HallC3×C52 ⋊ C4×C7×C11
HallC52×C7×C11 ⋊ Dic3
HallC3×C52×C11 ⋊ C4×C7
HallC3×C52×C7 ⋊ C4×C11
HallC52×C11 ⋊ C7×Dic3
HallC3×C7×C11 ⋊ #1043
HallC52×C7 ⋊ C11×Dic3
HallC3×C11 ⋊ C7×#1043
SylowC52 ⋊ C7×C11×Dic3
HallC3×C7 ⋊ C11×#1043
SylowC3 ⋊ C7×C11×#1043

Subgroups

subgroupG/H
center, hypercenterC7×C11C3⋊#1043
commutator, hypocenterC3×C52C4×C7×C11
FrattiniC1G
Fitting, socleC3×C52×C7×C11C4
prime radicalC3×C7×C11×C5⋊D5C2
cosocleC3×C5⋊D5C2×C7×C11
LCSG ▷ C3×C52
UCSC1 ◁ C7×C11

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5775

Conjugacy classes & character table

1848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 533);