Finite Group Databasebeta

C2×C22⋊#10596833 #17989554

order4672
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊#10596833

Splittings

SylowC73 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC23C2×#64408
commutatorC2×C73C22×C8
FrattiniC22C22×#64408
Fitting, prime radicalC24×C73C4
socleC23×C73C2×C4
cosocleC2×Dic73C23
hypercenterC24#64408
hypocenterC73C2×C22⋊C8
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C24

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4672, 1516);