Finite Group Databasebeta

C2×#28410462 #44416725

order29248
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23

Aliases

direct productC2×#28410462

Splittings

SylowC457 ⋊ C2×#97

Subgroups

subgroupG/H
centerC22×C4C2×D457
commutatorC2×C457C2×C42
FrattiniC2×C4C22×D457
FittingC22×C8×C457C2
socle, prime radicalC23×C457C2×C4
cosocleC2×C4×C457C23
hypercenterC22×C8D457
hypocenterC457C2×#97
LCSG ▷ C2×C457 ▷ C457
UCSC1 ◁ C22×C4 ◁ C22×C8

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29248

Conjugacy classes & character table

7336 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29248, 497);