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C2×C49×C11⋊D11 #37557383

order23716
automorphism?
homologyAbelianization (H1) = C22×C49 · Schur multiplier (H2) = C2×C11

Aliases

direct productC2×C49×C11⋊D11
unambiguous semidirect product(C2×C11)⋊(D11×C49)

Splittings

FittingC2×C112×C49 ⋊ C2
derived, SylowC112 ⋊ C22×C49
HallC112×C49 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C49C11⋊D11
commutator, hypocenterC112C22×C49
FrattiniC7C2×C7×C11⋊D11
FittingC2×C112×C49C2
socleC2×C7×C112C2×C7
prime radicalC2×C7×C11⋊D11C7
cosocleC7×C112C22×C7
LCSG ▷ C112
UCSC1 ◁ C2×C49

210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11858

Conjugacy classes & character table

6076 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23716, 46);