Finite Group Databasebeta

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C7×(C11⋊C5)⋊#595 #39910404

order26180
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×(C11⋊C5)⋊#595
unambiguous semidirect product(C11⋊C5)⋊(C7×#595)
unambiguous semidirect product(C11⋊#595)⋊(C5×C7)
unambiguous semidirect product(C7×C11⋊#595)⋊C5

Splittings

Fitting, socle, HallC7×C11×C17 ⋊ C4×C5
derived, HallC11×C17 ⋊ C4×C5×C7
HallC7×C17×C11⋊C5 ⋊ C4
HallC7×C11⋊#595 ⋊ C5
HallC17×C11⋊C5 ⋊ C4×C7
HallC11⋊#595 ⋊ C5×C7
HallC7×C11⋊C5 ⋊ #595
HallC7×C17 ⋊ Dic11⋊C5
HallC7×C11 ⋊ C5×#595
HallC11⋊C5 ⋊ C7×#595
SylowC17 ⋊ C7×Dic11⋊C5
SylowC11 ⋊ C5×C7×#595

Subgroups

subgroupG/H
center, hypercenterC7(C11⋊C5)⋊#595
commutator, hypocenterC11×C17C4×C5×C7
FrattiniC1G
Fitting, socleC7×C11×C17C4×C5
prime radicalC7×D17×C11⋊C5C2
cosocleC11×D17C2×C5×C7
LCSG ▷ C11×C17
UCSC1 ◁ C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1309

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26180, 26);