Finite Group Databasebeta

C2×#15688949 #20245165

order6016
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#15688949

Splittings

SylowC47 ⋊ C2×#366

Subgroups

subgroupG/H
centerC23D376
commutatorC8×C47C22×C4
FrattiniC2×C8C22×D47
FittingC22×C16×C47C2
socleC23×C47D8
hypercenterC22×C16D47
hypocenterC47C2×#366
LCSG ▷ C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

168 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1516 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#26103978, #26103979, #26103996, …
maximal normal subgroup of#26103978, #26103979, #26103996, …
maximal quotient ofC2×#20241460, #26127920, #26127959, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6016, 6287);