Finite Group Databasebeta

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C7×C3⋊(C11⋊#1043) #37528723

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

Aliases

direct productC7×C3⋊(C11⋊#1043)
unambiguous semidirect productC3⋊(C7×C11⋊#1043)
unambiguous semidirect productC11⋊(C7×C3⋊#1043)

Splittings

Fitting, socle, HallC3×C52×C7×C11 ⋊ C4
derived, HallC3×C52×C11 ⋊ C4×C7
HallC52×C7×C11 ⋊ Dic3
HallC3×C52×C7 ⋊ Dic11
HallC52×C11 ⋊ C7×Dic3
HallC3×C7×C11 ⋊ #1043
HallC52×C7 ⋊ Dic33
HallC7×C11 ⋊ C3⋊#1043
HallC3×C52 ⋊ C7×Dic11
HallC3×C11 ⋊ C7×#1043
SylowC52 ⋊ C7×Dic33
HallC3×C7 ⋊ C11⋊#1043
SylowC11 ⋊ C7×C3⋊#1043
SylowC3 ⋊ C7×C11⋊#1043

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C11⋊#1043)
commutator, hypocenterC3×C52×C11C4×C7
FrattiniC1G
Fitting, socleC3×C52×C7×C11C4
prime radicalC3×C7×C11×C5⋊D5C2
cosocleC3×C11×C5⋊D5C2×C7
LCSG ▷ C3×C52×C11
UCSC1 ◁ C7

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5775

Conjugacy classes & character table

1638 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 534);