Finite Group Databasebeta

C2×#28414051 #44442109

order29504
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#28414051

Splittings

SylowC461 ⋊ C2×#107

Subgroups

subgroupG/H
centerC23C22⋊D461
commutatorC4×C461C22×C4
FrattiniC2×C4C22×D461
FittingC2×C4⋊C4×C461C2
socle, prime radicalC23×C461D4
cosocleC2×C4×C461C23
hypercenterC2×C4⋊C4D461
hypocenterC461C2×#107
LCSG ▷ C4×C461 ▷ C2×C461 ▷ C461
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29504

Conjugacy classes & character table

4628 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29504, 582);