Finite Group Databasebeta

C2×#28410483 #44416807

order29248
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#28410483

Splittings

SylowC457 ⋊ C2×#106

Subgroups

subgroupG/H
centerC23C22⋊D457
commutatorC4×C457C22×C4
FrattiniC2×C4C22×D457
FittingC2×C4⋊C4×C457C2
socle, prime radicalC23×C457D4
cosocleC2×C4×C457C23
hypercenterC2×C4⋊C4D457
hypocenterC457C2×#106
LCSG ▷ C4×C457 ▷ C2×C457 ▷ C457
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 29248

Conjugacy classes & character table

4588 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29248, 579);