Finite Group Databasebeta

← Prev (#41003968) Next (#41003970) →

C7×D7×C11⋊C25 #41003969

order26950
automorphism?
homologyAbelianization (H1) = C2×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×D7×C11⋊C25
unambiguous semidirect productC7⋊(C2×C7×C11⋊C25)
unambiguous semidirect product(C11×D7)⋊(C7×C25)
unambiguous semidirect product(C7×C11×D7)⋊C25

Splittings

derivedC7×C11 ⋊ C2×C7×C25
HallC72×C11⋊C25 ⋊ C2
HallC7×C11×D7 ⋊ C25
HallC72×C11 ⋊ C2×C25
SylowC72 ⋊ C2×C11⋊C25
SylowC11 ⋊ C7×D7×C25

Subgroups

subgroupG/H
center, hypercenterC5×C7D7×C11⋊C5
commutator, hypocenterC7×C11C2×C7×C25
FrattiniC5C7×D7×C11⋊C5
Fitting, socleC5×C72×C11C2×C5
prime radicalC5×C7×C11×D7C5
cosocleC5×C7×C11C2×C5×C7
LCSG ▷ C7×C11
UCSC1 ◁ C5×C7

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3850

Conjugacy classes & character table

1225 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26950, 36);