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C2×D49×C121 #37557345

order23716
automorphism?
homologyAbelianization (H1) = C22×C121 · Schur multiplier (H2) = C2

Aliases

direct productC2×D49×C121
unambiguous semidirect productC49⋊(C22×C121)
unambiguous semidirect product(C2×C49)⋊(C2×C121)

Splittings

FittingC2×C49×C121 ⋊ C2
derived, SylowC49 ⋊ C22×C121
HallC49×C121 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C121D49
commutator, hypocenterC49C22×C121
FrattiniC7×C11C2×C11×D7
FittingC2×C49×C121C2
socleC2×C7×C11C11×D7
prime radicalC2×C11×D49C11
cosocleC11×C49C22×C11
LCSG ▷ C49
UCSC1 ◁ C2×C121

45 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11858

Conjugacy classes & character table

6292 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23716, 8);