Finite Group Databasebeta

C22×#11924018 #17989363

order4672
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×#11924018

Splittings

SylowC73 ⋊ C22×Q16

Subgroups

subgroupG/H
centerC23C22⋊D73
commutator, cosocleC4×C73C24
FrattiniC4C23×D73
FittingC22×Q8×C73C2
socle, prime radicalC23×C73D4
hypercenterC22×Q8D73
hypocenterC73C22×Q16
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4672, 1325);