Finite Group Databasebeta

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C7×C11×D7×C25 #41003974

order26950
automorphism?
homologyAbelianization (H1) = C2×C7×C11×C25 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, HallC72×C11×C25 ⋊ C2
derivedC7 ⋊ C2×C7×C11×C25
HallC72×C25 ⋊ C2×C11
HallC72×C11 ⋊ C2×C25
SylowC72 ⋊ C2×C11×C25

Subgroups

subgroupG/H
center, hypercenterC7×C11×C25D7
commutator, hypocenterC7C2×C7×C11×C25
FrattiniC5C5×C7×C11×D7
FittingC72×C11×C25C2
socleC5×C72×C11C2×C5
prime radicalC5×C7×C11×D7C5
cosocleC5×C7C2×C5×C7×C11
LCSG ▷ C7
UCSC1 ◁ C7×C11×C25

66 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3850

Conjugacy classes & character table

9625 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26950, 41);