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C2×C11×D301 #27210380

order13244
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D301
unambiguous semidirect product(C2×C7)⋊(C11×D43)
unambiguous semidirect product(C2×C43)⋊(C11×D7)

Splittings

Fitting, socleC2×C7×C11×C43 ⋊ C2
derived, HallC7×C43 ⋊ C22×C11
HallC7×C11×C43 ⋊ C22
HallC11×C43 ⋊ C2×D7
HallC7×C11 ⋊ C2×D43
SylowC43 ⋊ C2×C11×D7
SylowC7 ⋊ C2×C11×D43

Subgroups

subgroupG/H
center, hypercenterC2×C11D301
commutator, hypocenterC7×C43C22×C11
FrattiniC1G
Fitting, socleC2×C7×C11×C43C2
LCSG ▷ C7×C43
UCSC1 ◁ C2×C11

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3344 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13244, 28);