Finite Group Databasebeta

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C7×C3⋊(C11⋊#1181) #40999652

order26796
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊(C11⋊#1181)
unambiguous semidirect productC3⋊(C7×C11⋊#1181)
unambiguous semidirect productC11⋊(C7×C3⋊#1181)

Splittings

Fitting, socle, HallC3×C7×C11×C29 ⋊ C4
derived, HallC3×C11×C29 ⋊ C4×C7
HallC7×C11×C29 ⋊ Dic3
HallC3×C7×C29 ⋊ Dic11
HallC11×C29 ⋊ C7×Dic3
HallC3×C7×C11 ⋊ #1181
HallC7×C29 ⋊ Dic33
HallC3×C29 ⋊ C7×Dic11
HallC7×C11 ⋊ C3⋊#1181
HallC3×C11 ⋊ C7×#1181
SylowC29 ⋊ C7×Dic33
HallC3×C7 ⋊ C11⋊#1181
SylowC11 ⋊ C7×C3⋊#1181
SylowC3 ⋊ C7×C11⋊#1181

Subgroups

subgroupG/H
center, hypercenterC7C3⋊(C11⋊#1181)
commutator, hypocenterC3×C11×C29C4×C7
FrattiniC1G
Fitting, socleC3×C7×C11×C29C4
prime radicalC3×C7×C11×D29C2
cosocleC3×C11×D29C2×C7
LCSG ▷ C3×C11×C29
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6699

Conjugacy classes & character table

1869 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26796, 85);