Finite Group Databasebeta

C2×C22⋊#16814532 #44416738

order29248
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊#16814532

Splittings

SylowC457 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D457
commutatorC2×C457C22×C8
FrattiniC2×C4C22×D457
FittingC23×C4×C457C2
socleC23×C457C2×C4
prime radicalC24×C457C4
cosocleC2×C4×C457C23
hypercenterC23×C4D457
hypocenterC457C2×C22⋊C8
LCSG ▷ C2×C457 ▷ C457
UCSC1 ◁ C22×C4 ◁ C23×C4

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14624

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, 510);