Finite Group Databasebeta

C2×C22⋊#16814779 #44442037

order29504
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊#16814779

Splittings

SylowC461 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D461
commutatorC2×C461C22×C8
FrattiniC2×C4C22×D461
FittingC23×C4×C461C2
socleC23×C461C2×C4
prime radicalC24×C461C4
cosocleC2×C4×C461C23
hypercenterC23×C4D461
hypocenterC461C2×C22⋊C8
LCSG ▷ C2×C461 ▷ C461
UCSC1 ◁ C22×C4 ◁ C23×C4

202 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14752

Conjugacy classes & character table

7400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 510);