Finite Group Databasebeta

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C3×C7⋊(C11⋊#1043) #37528633

order23100
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC3×C52×C7×C11 ⋊ C4
derived, HallC52×C7×C11 ⋊ C3×C4
HallC3×C52×C11 ⋊ Dic7
HallC3×C52×C7 ⋊ Dic11
HallC52×C11 ⋊ C3×Dic7
HallC3×C7×C11 ⋊ #1043
HallC52×C7 ⋊ C3×Dic11
HallC7×C11 ⋊ C3×#1043
HallC3×C52 ⋊ Dic77
HallC3×C11 ⋊ C7⋊#1043
SylowC52 ⋊ C3×Dic77
HallC3×C7 ⋊ C11⋊#1043
SylowC11 ⋊ C3×C7⋊#1043
SylowC7 ⋊ C3×C11⋊#1043

Subgroups

subgroupG/H
center, hypercenterC3C7⋊(C11⋊#1043)
commutator, hypocenterC52×C7×C11C3×C4
FrattiniC1G
Fitting, socleC3×C52×C7×C11C4
prime radicalC3×C7×C11×C5⋊D5C2
cosocleC7×C11×C5⋊D5C2×C3
LCSG ▷ C52×C7×C11
UCSC1 ◁ C3

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5775

Conjugacy classes & character table

1626 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 444);